We have taken several very good trips to the Cross Bay/Long Island area.  It is a nice area with small lakes, good campsites, and a strong chance of seeing moose.  I don't know how much paddling you want to do, but a side trip to Frost Lake is a possibility, and it would be early to swim, but there is a beautiful campsite on Frost Lake with a lovely sand beach.  Scenic even if you don't swim.

The southern site on Cross Bay is a nice one, and there are several good sites on Long Island.  I understand that there is a good site on the island, but we haven't stayed there.

Gordon has a nice campsite, and of course if you can get down to Cherokee you have the option of some very good sites and one of the most beautiful lakes in the BWCA, IMHO.

In our experience, in mid-June this area is not particularly crowded, and the campsites would be available with no problem unless you paddle very late in the day. 

I cannot speak to fishing, as we do not fish.

Not all Quiet Journey members are quite as dismissive of the BWCA as the previous post might lead you to believe.  Some of us do, in fact, love the BWCA and plan to continue tripping there.  And that doesn't mean that we have never experienced the Quetico, either.