I personally had good experience playing the Pathfinder card game with my partner. You choose from one of the characters' decks, taking on their unique items/stats then each game session you play lasts maybe half an hour to an hour. You may find loot along the way which your character keeps for the game next session. Your characters level up along the way, allow you to do things like, say, roll a D6 on attack instead of a D4. Of course the monsters get more difficult along the way as well. There's a simple overworld map and story line to follow so you can track your progress along the way.

There's also a pen and paper version of Pathfinder which I think makes a gentle introduction into the DnD world for those looking to explore that genre but don't necessarily want to dive in head first.

You might like Gloomhaven: Jaws of the Lion. You pick your characters, then do quests (which can branch). Pretty sure it uses a book for the scenario maps, so the set up will be figuring out your characters deck and items. The game supports up to 4 people, but you could also just play multiple characters (if you want).

It may be a little old (hard to find)and slightly more rules-heavy than you're looking for, but Last Night on Earth is great. It's zombies vs human survivors in different scenarios.

Pandemic is also great. It's a coop game where the players are trying to eradicate disease around the globe.

Since you seem to be also speaking german: Adventure Games: Im Nebelreich is a really charming and cute game which is perfect for 2 players and should be exactly what you're looking for. Be sure to install the app beforehand and download the narration

Stuffed Fables, or The Adventures Of Robin Hood (not played the latter but I believe it's a similar adventure gamebook system)

TINY EPIC DUNGEONS is a highly portable medium complexity cooperative fantasy dungeon crawler. Good for camping, but the RPG elements are more in the loot-and-level-up style than the epic narrative style.

ARKHAM HORROR LCG is a fairly portable light-medium complexity cooperative card game set in the Cthulhu mythos. There is a surprising amount of narrative for a card game, with some leveling-up between stories. And a seemingly neverending supply of story expansion decks.

FORGOTTEN WATERS is a full size light complexity cooperative boardgame with a pirate theme. I haven't played this one yet, but by all accounts it has a great story.

None of these games require significant preparation or a GM. Forgotten waters has an app, but I don't remember if it's required to play the game.

Check out Sleeping Gods.

You can play a simple one-shot system like "Lasers and Feelings" or "Scrolls and Swords"

• It's free (Sci-fi or Fantasy [direct PDF])
• There are few components (just need some 6-sided dice)
• You can play for as long or as little as you like
• It's no prep -> you make it up as you go!
• Perfect for camping

I don’t think you’ll find a good RPG that works for camping. Check out My City, it’s a smaller campaign style polyomino game that has an ongoing series of missions.