I have two ideas:
1. Items or abilities that the player can get which can be preserved through skillful play, but which can be damaged and rendered unusable or much less effective through less skillful play. These can be repaired by some in-game mechanic for free (in real money) but take time to do so. Players can pay real money for an instant fix. They can play the game either way, but may not be able to access certain areas or will just have a harder time without the items or abilities.
For this I'm inspired by the Master Sword from Link to the Past, where if you keep your life meter full it shoots beams. But if you make a mistake and take a hit, the sword is still good but suddenly less effective than you know it can be. I like mechanics like this because you can have everything without spending any money but in exchange you have to become good at the game. I get double satisfaction-- I'm good at the game, and my skill lets me enjoy "deluxe" features for free!
2. Minions! I always love having commandable minions in a single player game. A minion might be able to do dull tasks for the player (like rounding up arrows or other disposable items, with some exposure to danger while getting them) or maybe accompany the player in dungeons. Minions can be developed by grinding, just like the player character, but the player might also be able to just buy a better minion right from the start.
I never like the idea of having features locked away because I haven't paid, such as dungeons and equipment, even in a F2P game where that sort of attitude doesn't make sense. I feel a greater sense of investment from my time than from a few dollars, and if I've played every part of a game that's available for free it always rankles a bit to have to go through the formality of spending a couple bucks for what feels like such a small expansion of the experiences I've already had. If I get almost the whole game for free, it's odd to pay $2 just for a grappling hook.