You'll need a boat to get to anything worthwhile, I'm pretty sure. I was just down at Sugarloaf Key in late June. We rented a boat and did several dives off Key West. Red Marker 32 (aka Toppino's) is not far out to the south from Key West, has three mooring balls and is a shallow spot on the edge of the reef, 30' or so max. There's good structure and lots of fish when we were there. There are many similarly close reef and wreck spots, if you have a boat. You can find their names via google, but from what I've seen you can't trust the GPS numbers that are posted online. I don't believe we found a single spot, of six or so we checked, that was anywhere near accurate.
If you go with a charter outfit, they'll take you to good spots. Looe Key is a particularly nice reef spot, a Reserve with oodles of fish, a bit north of Key West, 30 ft or less as well. The best option for there is to go with a dive op on Big Pine Key, 30 miles north. I've done Strike Zone, Innerspace, and Looe Key Resort and liked Looe Key Resort the best. It's also slightly closer to KW. LKR and Strike Zone are big boats with lots of snorkelers, but we got 60+ minutes on each of the two dives, with LKR. They were also a bit better price I think. Innerspace likely uses a smaller boat (it did a couple years ago), but based on one trip, I'd make sure I understood what their bottom time policy was, in advance.
There are lots of wrecks out of Key West as well, if that's of interest.