Go out on one of the snorkel boats. Best spots are about 7 miles south of Key West (outer reef). Not a whole lot to see off of the shore in Key West.
One spot I go to from time to time is easy to get to by car. If you go past the NAS (Naval Air Station) heading north from Key West, you will come to a Circle K gas station on the right. Turn right on Boca Chica Rd and follow it to the end. At low tide, there will be some exposed rock about 0.25 miles SW of the end of the road. Swim to those and then head straight out. There are scattered patch reefs. FYI, you definitely must have a dive flag. You will be in 6-8 feet of water and boats do run along the coast. Best spots are about 0.5 miles from shore, so not for the weak swimmer.