I will be traveling w/ my family from Ft. Lauderdale to Key West in early July. We have allowed 2 days for a visit to the Everglades but did not initially consider the "bug" issue.
How bad are the bugs there in July?
Any suggestions of a place to stay?

The Everglades will be buggy in July. You don't say what you planned to do for 2 days but you may decide to spend just part of a day there. With long sleeves/pants and bug spray, you should be okay. If you are traveling from FtL to KW, you would enter the park at the south entrance. There is a nice visitors center and the Anhingua Trail is not far from the entrance. Try to hook up with a ranger led talk. The only place to stay in that part of the Everglades is Flamingo (search for discussions of Flamingo). Rather than stay there, I would drive on to Key Largo and/or Islamorada in the Keys. If you family includes kids in the 3-7 grade range, read Freedom River by Marjory Stoneman Douglas or Talking Earth by Jean Craighorn George for 'Glades background.