I agree that the interior trails are fantastic. My cousins lived on the island when I was a kid, and we explored the interior of the island as much as the coast and the town--just running around as kids will do. There's the natural bridge of course, and there were some cliffs, caves and stuff too. Mountain bikes would probably be fun, but unfortumately I've only ridden the rental bikes there. If you do rent, a tandem might be a pleasant change of pace, especially on your anniversary.