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