Not much in Havasu to be honest. London Bridge is the bridge to the island, so you'll see it without any problem. If you like to golf, there are several courses in the area that you can swing away on. There is a couple of bars right around the bridge and marina that are usually fun to hang out at.
The Grand Canyon isn't too far off, easy day drive. Havasu Falls is a day long excursion that has some really awesome views and sapphire blue water (5 mile hike in and out though). Hoover Dam & Parker Dam are in the area. Never been to Parker, but the Hoover Dam is a really cool tour.
Boating, golf and desert scenery is really about it. The biggest draw for Lake Havasu is that it is a lake in the middle of the desert. Not a whole lot around it really.