The best time to visit the Boundary Waters is every time you can! May the temperatures can be chilly and fishing for lake trout and walleye can be very good depending upon when the ice went off of the lakes. June is also a good fishing month and smallmouth start biting around the 2nd week, with walleye and lake trout still biting strong until the water warms up too much. Northern pike tend to bite all of the time and how the fishing is the rest of the summer depends upon water levels, temperatures and the skills of the angler.
If you're looking for berries, June is for strawberries and the end of July or August are good for blueberries and thimbleberries. Wildlife is most abundant in May and then again in the fall, but you'll always see loons, eagles and plenty of ducks.
Whenever you can get away to the BWCA is the best time to come!