Here's what we like when we are there.
For breakfast, head one street over from Duval and go to Blue Heaven. You eat outside and chickens roam around the table while you eat. They don't bother you though. The Banana Pancakes are the BEST!!
For lunch, if you like seafood (which you better if you are going to Key West!!

) Turtle Krawls has the best conch fritters. And it's a nice walk by the water to get there.
Crabby Dicks is really good food also, that's right on Duval and you eat upstairs overlooking the street.
As for bars, where do I start, every other building is a bar, with a T-shirts shop between!

We really like Irish Kevin's, but be prepared, the entertainment is a VERY raunchy singer/comedian. Don't go if you are easily offended! Fat Tuesday has some great frozen drinks. They are premade, and spinning in machines, like Slurpees at 7-11. Just point to the one you want. Quick serve!!
For sightseeing, I would take the Trolley Tour around the island. Make sure it's the round trip one where you can get off and back on at the different stops. There's a fort and museum over by Smather's Beach that is pretty interesting.
Also, beware of the cheap T-shirt shop owners. You pick your shirt and they put on whatever screen print you choose. Make sure you know the price upfront, or they will change it on you after it's printed. Stand your ground and argue with them or they walk all over you. Most of them don't speak much English. If you want nice souvenier T-shirts, I would go to store where they are already printed. You can pretty much tell by the looks of the store what you will get.
Also, if you are not from a big city and don't have much diversity in your area (I'm from a little town of 3,000) keep an open mind! I'm pretty open-minded, but my hubby isn't. One of my favorite parts of our trip (unlike my hubby) was going into one of the gay bar/drag shows and watching the drag queens up on stage. They are so funny! But that's the night life, you don't see that during the day.
Where are you staying while you are there? We stayed in a B&B right on Duval. It was very nice. We parked our car and never used it the whole week. We walked everywhere.
Oh, one more thing, The Hemingway House Tour was pretty interesting and I will 2nd the Mel Fisher Museum as something to see. Go to Mallory Square for Sunset Celebration each night and see the crazy Cat Man and his trained cats. Gosh, so much to do. When you get there, buy a guide book or ask the locals, they will give you some more great ideas!!
Have a great time!!