What you encounter depends upon the route you select
and when you travel. Campsites that are easily accessible
by hikers will usually be full or nearly full before the end of
the day. Campsites that are easlily accessible by boaters
will usually be taken early in the day (and expect noise).
But, there are some campsites hidden on the inner lakes
that that are only lightly used, even during the peak in
July/August.

I took a solo canoe trip on the island a few years ago
during the second week in August and spent many nights
where I was the only camper on an entire lake! These
interior canoe campsites are rustic (no inprovements
except discreetly hidden outhouses). If you have
backpacked the island, you know what I mean.

Here is my route with some comments:

Daisy Farms
 crowded, boaters, I got the last campsite (I was trying to
 make Moskey Basin, but battled a headwind all day)

Intermediate Lake
 all by myself, rustic, a hard day to get here, but I left
 the crowd behind

Wood Lake
 all by myself, stunning rustic campsite on a bluff

Lake Whittlesey
 all by myself, saw two canoes (day trippers) next day

Lake Richie
 one other couple (at the rustic canoe campsite)  

Chickenbone Lake West
 crowded campsite (almost had to share with a ranger)

McCargoe Cove
 moderate crowd, boaters, beautiful cove and moose,
 lots of shelters

Pickeral Cove
 only one campsite, many others passing through

Belle Isle
 lots of boaters, yakkers, ranger station, nice shelters
 and agate beach

Lane Cove
 a few hikers, this is a lightly used campsite all season
 beautiful view of the big lake and islands. I always get
 to Lane Cove when I go to IRNP.

Duncan Narrows
 lots of boaters, shelters, nice sunset

Duncan Bay
 all alone, nice campsites with shelters on a little point
 it has a boat dock, but the gas types are afraid they'll
 bend their props getting to it

Rock Harbor
 grand central station, but I wanted chocolate milk and
 a shower on the last day

I have had campsites to myself when backpacking in
September (Hatchet Lake, Island Mine, Lake Desor, Little
Todd) - my favorite time for IR. Still warm, no bugs,
fewer other people.

I hope that this helps you get a better feel for the interior.

-aj