Take the Conch Train (20.00 each), it takes you around to all the main sights. Be sure you go to Mallory Square in the evening for the street performers and Key West sunset. There's a lot to see within short distance of the ship.
You could rent an electric car and go sight seeing around the island. I've done the conch train twice, and I truly think my 7 year old would be bored on it...I was after about a half hour. We did it the second time because our friends wanted to and I was really bored on that one not to mention they pack you on that train like sardines. We are going to key west in October and are considering the electric car thing. We aren't traveling with our kids so we may opt for the bar crawl up Duval street. Also don't miss the Key lime pie!
Just enjoy the ambiance of Key West. Go to Hemingway's house. Your 7 yoa will enjoy all the cats. Just walk around and look at the great old houses. Go to the Southernmost Point and look for Cuba. (You can't really see it. It's 90 miles away.) If you are there at sunset enjoy the party. Watch the Cat Man with his trained cats. Go to the top of the Lighthouse and see all of Key West. Go to Lou Fisher's museum and hold a gold bar from the Spanish ship the Atocha in your hand. Too bad you can't pull it out of the case. All of these are within walking distance of the dock. Key West is a small island. Key West is wonderful!!! If you are going in the summer it is going to be very, very hot. Make sure you put on sun tan lotion, wear a wide brimmed hat and carry water. The aquarium is very small but you can touch the horseshoe crabs in the tank. If you want a different drink try a Mohito. It is rum, simple syrup and mint leaves which are crushed and then poured over ice. Strong but good. The conch train is OK but it is a long ride and really not that interesting for a child. As you can tell Key West is one of my very favorite places. If you didn't have your child with you I would tell you to go to Sloppy Joes, Capt. Tony's and if you are adventurous, Atlantic Shores for a taste of the alternate life styles. You will love Key West. Have a wonderful time.