There are not so many options on where to go, especially in the long run (I like playing the same world for decades of game time). I'd like to list what I have tried and ask the community to discuss it, and maybe someone would provide more ideas.
Random encounters
Deadly at start. Can be a fun challenge if your world has enough biome and/or modded-in creature diversity. After you're geared up and trained, they eventually become boring, even though the risk is still there...
Beast-hunting
Under this I mean hunting for semi- and megabeasts. Easily moddable so you'll face packs of enemies. My main concerns here are too simple terrain and therefore inability to employ complex tactics, and also limited amount of beasts to fight. Besides, many of the beasts have missing limbs from worldgen, and that removes part of fun.
City rampaging
Elf-killing sprees and anti-goblin crusades all go here. Towns offer the best battlefields, with obstacles and cover and such. There are only so many civ members in the world though, and... well, I'm not really into playing a psychopathic murderer.
Visiting abandoned forts
You're very limited with making non-monster challenges, since adventurers can't jump or climb yet, nor can they interact with pressure plates. Also, since you would have designed it, you'd know how to bypass it anyway. So, HFS and sieges aside, it only makes fun if the site has a chasm. Then, if the fort is reasonably deep underground, upon your every visit it will be infested with chasm creatures - since any underground tile is suitable for their spawning. Nearly ideal because this is an unlimited source of monsters, and forts may provide unusual environments to fight in.
Maybe cave rivers work like that too. Does anyone know if it's so? Right now I'm thinking about turning such a river into an underwater labyrinth with pockets of air here and there, and hoping for amphibious monsters to spawn inside when you visit it in adventure mode. Also, gotta check if adventurers can operate pumps...