We have sailed from ft Myers to the Dry Tortugas several times. It is an easy doer but, as mentioned by others, there is no amenities there other than what nature has provided. I have traded with the fisherman there for just about anything from diesel to fish.
From Tampa, depending on how you want to sail, there are a plethera of anchorages enroute to the Keys. Egmont Key, Anna Maria Isl, Saratsota Bay, Venice city dock, Charlotte Harbor (Boca Bayou, Pelican Bay/Cayo costa, Useppa, etc), Ft Myers Beach (north or south end), New Pass, Gordon Pass (Naples), Marco Island (Factory Bay or the Winn Dixie), Little Shark River, Marathon, Etc.
If sailing overnight I usually enter the park at the Tortugas at the northern most yellow bouy then head due south to the west side of the fort and around the south side of the fort to the east side. You are only allowed to anchor overnight on the east or south side of the fort. Holding is fair to good. As previously mentioned, if the wind blows more than 15-20 there can be significant activity in the anchorage. Many who venture there seem to think that 3:1 rode is good enough. If the weather has been poor or winds from the east the anchorage tends to fill up with those waiting to head towards Key West.
If you do head towards Key West and find that you are running out of time to make it by dark you can anchor anywhere around the Marquesas which is about 30 miles from Key West. Watch your depth, as always, and don't worry about the bombing range off the west of the Marquesas. they have used it for years and even when they did they missed a lot.
If you need more info just drop me a note. I sailed out of Ft Myers for the last 8 years and can help you find services or anchorages if you want.