First, let me say that I'm not going to tell you how to get to the best off-trail campsites or fishing lakes on the Island.  I'm also not going to tell you the easiest way to get, off-trail, from one specific place on the Island to another.  I don't like directing potentially inexperienced wilderness hikers to places where they may get lost, or worse.  Read on for some useful info, though:

Basics of Cross-Country Travel on Isle Royale
Isle Royale offers a wide variety of terrain to explore, with an equally wide variety of vegetation.
1.    Ridges
    Ridgetops are often the easiest places for cross-country travel on the Island.  Depending on where you are, you'll usually find mixed aspen and conifer stands, or even sugar maple/yellow birch stands (at the west end of the Island).  Interspersed with these stands, especially toward the middle and east ends of the Island, can be areas of open rock, low brush, blueberries, juniper, and so forth.  These open areas tend to run in discontinuous strips, usually a couple hundred feet wide or so, parallel to the ridgetops and usually on southeast-facing slopes at varying distances from the top of the ridge.  You can really cruise in some of these open areas.  More often, though, you'll find yourself navigating through moose-browsed aspen thickets which vary from pretty open to thick enough that you'll want to try cutting uphill or downhill to find an easier route.
2.    Perpendicular to ridges
    Isle Royale has a number of sheer, mostly north-facing cliffs on the north sides of ridges.  However, most north-facing slopes can be traversed without too much difficulty by exploring around a bit to find a way up or down.  The biggest travel problems encountered when travelling perpendicular to ridges are found in the low spots between the ridges, as explained next:
3.    Stream valleys and wetlands
    The vast majority of streams on Isle Royale run in the valleys between the WSW/ENE-oriented ridges, which created the majority of Isle Royale's topography.  The ridges are formed by the hardest rocks such as conglomerate and the most resistant portions of lava flows. Valleys are formed where rocks are less resistant to erosion.  Most Isle Royale streams that flow in the valleys between the ridges are fairly slow-moving, and most of those valleys are fairly wide, so they tend to be swampy, with scattered beaver ponds.  Wetlands in the valleys vary from cedar swamps to open wetlands.  All of these can be a pain to cross.  In addition, not all wetlands appear on the maps, especially the Trails Illustrated map and other maps of that scale.  I have found that many are not even shown on 7 1/2 minute topos.  So, expect the possibility of getting wet (knee deep or greater, very slow travel, and lots of trial and error in route-finding.
    Streams which run perpendicular to the ridges, however, are usually faster-moving and easier to cross, especially if they have a narrow valley.
4.    Lake Superior shoreline
    With few exceptions, the Lake Superior shoreline is a very difficult area for cross-country travel.  There are a few exceptions (e.g., Rainbow Cove), but in general, you'll find cliffs, boulders, blowdown, and brush.  With that said, they are some of the most spectacular places on the Island.  Much of the Island's south shore, from south of the east end of Siskiwit Lake east to about Lea Cove, has bare rock mixed with gravel and cobble beaches.  Going is very slow there, though, due to frequent cliffs which impede your progress.  Where I have explored the Island's north shore, such as north of Lake Desor, I've found thick forest growing on a steeply sloping hillside, with frequent huge boulders.
5.    Low ridges and flat areas without swamp symbols or streams shown
    These areas are highly variable.  You can encounter everything from open forest to bare rock  to unexpected wet spots to even cliffs.  Remember that a contour interval of 40 feet (as on the Trails Illustrated map can conceal a cliff nearly 80 feet high.

In summary, for those used to cross-country travel in open hardwood forests, you'll find Isle Royale a totally different world.  I probably average 2 mph travelling along ridgetops, and 1 mph crossing valleys and following lakeshores.

Backcountry permits are required to camp at other than designated campgrounds, but no permits are required to hike off-trail.  The Park Service, for good reason, discourages people from camping and hiking off-trail, for several reasons.  First, cross-country travel on Isle Royale is very difficult almost everywhere.  Second, there's the risk that inexperienced (or even experienced) cross-country travelers may become lost or injured, so a search and rescue operation may be necessary (Park Service folks have better things to do than hunt for someone who went into the wilds of the Island without adequate equipment, physical conditioning, or orienteering skills.  Third, cross-country travel and dispersed camping can cause damage to vegetation and disturbance to wildlife.  Finally, it's one more administrative issue for park staff to deal with.

With that said, cross-country travel, especially in the peak tourist season of July and August, can be the only way to have a true wilderness experience on the Island.

Backcountry camping permits can be obtained when registering for your backpack, canoe, or kayak trip.  Ask the Park Service person filling out your permit to look at a current backcountry zone map.  That map will tell which areas are open to dispersed camping at the time of year you will be there.  The Island is divided into about 50 backcountry zones.  In some zones (e.g., offshore islands), camping is never permitted.  Other zones are closed seasonally, while still others are always open.  The reason for the closure of most zones is the protection of nesting waterfowl and to provide solitude for wolves.

The Park Service staffperson filling out your camping permit will (hopefully) question your reasons for obtaining a backcountry permit, and may try to gauge your backcountry travel skills.  They should also evaluate the feasibility of your hike (Have you allowed enough time to make the trip you have planned, with plenty of time to spare?; It the place you tell them you're going to camp on a swampy lakeshore or a dry lakeshore; Does the travel route you show them on a map have you going up and down cliffs instead of circling around them?).  Questioning you like this is their job; they need to be sure you know what you're getting yourself into.

Don't be afraid to ask park staff for advice.  They're the experts about the Island, you (probably) aren't.  Don't play macho man (or woman) just because you know how to read a topo map.  If you have a lake in mind as a potential campsite, ask them what they know about it.  Not only will they be impressed by your conscientiousness and caution, but they'll feel a lot better about giving you the permit.  There are some nice lakeshores for off-trail camping, and some pretty miserable ones, too.  Without having been there, the odds are you can't tell which is which until you ask or actually go there.

Backcountry camping regulations
Here are a few rules and regs for backcountry camping:
1.    Camping is not allowed in zones where it is prohibited.
2.    Camping is not allowed on any islands, except the main island of Isle Royale, except at designated campsites.  The exception is for canoeists and kayakers caught by sudden severe weather.
3.    Backcountry campsites must be out of sight of water.  You may, however, leave your canoe or kayak along the shore (if it's hard to pull it up into the woods), and you may cook and eat meals along the lakeshore.
4.    Camping is not permitted within 1/4 mile of any trail or developed campground.  That's a real 1/4 mile, not what feels like 1/4 mile when walking through the woods.  If in doubt, pace it off (at least 500 steps in most woods), or walk for at least 7 or 8 minutes straight.  The main reason for the 1/4 mile rule is that people not camp within sight or sound of a trail or campground.
5.    You may not camp two consecutive nights in the same backcountry site.  You must move at least 1/4 mile each night before establishing a new camp.  This rule is in effect to minimize the chances that overused backcountry sites will develop
6.    You may only camp in backcountry zones for which you have a permit.  This does not mean that you have to camp in all of the zones you signed up for, or that you can't camp more than one night in a given zone if you just registered for one night there.  The reason for this regulation, I expect, is that in case you fail to come out of the woods when expected, folks will have some idea where to look for you.

While not a rule, I strongly recommend that you only camp out of sight and sound of others with backcountry camping permits.  The odds of seeing another person backcountry camping may be low, but if you do, give them their privacy.

I have applied for backcountry camping permits many more times than I've used them.  I usually use them as a backup, such as when I expect a campground may be full, or so I don't have to stay in that campground if it's noisy.

A few basic safety rules when backcountry camping
1.    Always let someone know where you expect to go.  If you don't want to be tied down all that much, at least give someone a general idea of where you're going so they know where to start looking for your body.
2.    Don't camp in moose trails or moose bedding spots.  In some places, these are the flattest, least vegetated spots, but don't be tempted.  Moose can't see worth a darn, and they can easily step on your tent (or canoe or kayak) by accident.  I've had them jump over my canoe and step within a foot of my head when I was in my tent.