Classic dungeon puzzles with switches, pressure plates, etc. Especially if there's hints instead of blind trial and error. Also adventure game like item combination puzzles are fine. Finding your way through a room of traps. Etc.
The Might and Magic series is good at putting this kind of stuff into dungeons. Especially making traps that require creative use of magic to get past: the old tile based titles had jump and teleport spells for a reason!
Playing cards or dice in a tavern is nice if the minigame is implemented well. Witcher is consistently good at that (Gwent, but also dice poker in the first game), and Arcomage is a fun game to play on its own even outside of M&M 7 (if you wanna play some Arcomage against other players, create a free account here:
https://arcomage.net/ I'm a regular player, have been on there for years).
Base management if it's engaging and/or impactful. BG2 had cool bases because which one you got depended on your character class, so the wizard would get a cool planar sphere and the fighter gets to rule a castle as its lord. Instead of annoying micromanagement you'd return there every couple of weeks, collect your taxes, and make a decision in an event (usually just a dialogue choice along the lines of "One of your apprentices fucked up, what do?" or "There's bandits in your fief, what do?"). Keep it lightweight, don't make it a chore. Make me feel like I'm the lord of some place, not the janitor.
Dicking around in town, doing stupid shit. Ultima VII is the prime example of that. Toss shit-filled baby diapers on Lord British to make him run away. Rob the bank despite being the avatar of virtue. Mess with the guards by putting out streetlights at night. Seriously, modern games can't hold a candle to Ultima VII's interactivity. You can do so much stupid shit in that game, it's glorious.
Now here's some non-combat stuff in RPGs that I absolutely
do not like:
Crafting. It's just a boring grind of collecting 2304 pieces of copper ore and 3413 pieces of tin ore so you can smelt them into bronze ingots so you can forge a generic bronze sword +5. Just have a boss enemy in a dungeon drop a magic bronze sword, that feels a lot more rewarding and cuts out a lot of grind. Extra negative points if your game features an unskippable mining animation when mining ore (looking at you, Skyrim). Crafting is a boring grind of generic resource farming which doesn't fit into the RPG gameplay loop at all. It makes exploration and combat less rewarding because instead of getting that juicy +5 sword as a drop from an enemy, or finding it tucked away in a dark corner only reachable with levitation, you find generic [insert metal type] ore clumps all over the place and collect enough of them until you can forge the sword yourself. Meh.
