Can't help you with a fishing recommendation, since I wasn't a fly fisherman when we visited that area early last year. However, you will be hard pressed to beat the grouper sandwich (for size and taste) at the Island Grill (
Island Grill, Best Islamorada Restaurant, Florida Keys).
If it's your first time to the Keys and you want to do something touristy, visit Robbies (
Feeding Tarpons at Robbie's) to feed the tarpon. The power of their jaws will surprise you.
As for a rod, if you hurry, you can buy a 9 wt St. Croix Imperial which currently only has an $80 bid on it.
St Croix Imperial Fly Rod 9' 9wt 2 Piece and Okumo Reel and Line | eBay
Good luck!