Summer locations

What destinations in the Midwest would I be able to climb at during the summer without dying of heat or bugs?

Devil's Lake is usually your best bet. There are usually very few skeeters. Can't do nothing about the heat and humidity but you have the nice clean lake to take a cool dip into after getting sweaty climbing and especially if you climb on the East Bluff at any of the areas down near the RR tracks. Pick breezy and in the shade spots to climb at on the worst days and you will be fine and better off then any other spot in Wetsconsin during the summer months.

How do you define "Midwest"? If you are buried in MO, it might be just as easy to head West as North ....

North shore of Minnesota

North shore of MN is very pleasant pretty much all summer, and if it does get too hot, a dip in superior's 55 degree water will cool you off

What are the recommendations for climbing areas in MN? How is South Dakota in the summer?

The specific crags on the north shore are probably shovel point and palisade head, though there are others, like carlton peak and ely's peak though both are farther away from the lake so bugs and heat are more likely