I love playing Skyrim with certain challenges. For example:
Survival Master Difficulty with disabled compass and map. It makes the Skyrim wilderness a much more ruthless and immersive place.
Or trying unusual character playstyles:
Get Lydia (or any other Follower) as quick as possible and play Healer only (Multiple Follower Mod recommended
Play a hand to hand combatant. Good options to make it viable are a Khajiit for the claw damage, getting vampirism for extra hand to hand damage and getting the pugilists gloves. Extremely powerfull, especially if you you choose to play a lvl1-only character.
playing without any equipment and items (maybe get some unenchanted clothes, so you don’t run around naked). Your best bets are probably a mage build, maybe Bretons with atronach stone for magic defense.
I love playing Skyrim with certain challenges. For example: