Jeremy,

If you choose your entry point and route wisely I think your biggest concern for a June trip will be bugs, especially if you or your wife is not very tolerant. I took my wife on her first trip to Quetico this June,  she did good except she was quite bothered by mosquitoes and black flys. Ticks can be bad in June also. Bugs  were not bad while on the water but it was hot and there was never much of a  breeze which made the bugs in camp very bad, even for me. She tried the OFF brand clip on but it seemed only to work if she was very stationary. I've not tried soaking my clothes as suggested, but head nets, long sleeves, pants tucked into socks, spending most of your time on the water, deet, campfire smoke, and catching fish seem to reduce my irritation level. If you plan on them, fearing the bugs shouldn't prevent a trip.

On our first couple of trips we had an outfitter drop us off at Beaverhouse Lake and we paddled east to Nym Lake. From the public phone at the landing we then called the outfitter for a pick up. It's an easy trip,  paddling with the prevailing wind, as long as they don't prevail too heavily, good campsites, only a few portages, good fishing and even a pictograph or two.  We saw a few other canoe trippers near the put in and take out, but only one or two during the middle of the week.

Many others here have much more experience that I, but send me a PM if you'd like more details on my route suggestion.