I enjoy combat in my games but what I mainly look for is the story aspect. I'm not the greatest role player but I have a lot of fun just playing with story in games, figuring out mysteries, and trying to find fun ways to solve problems that might arise.
I've ran games ranging from level 3 (I hate levels 1 and 2) to level 30 and I generally run games in my own world because it just give me more freedom to shape the game the players and I wish. I am open to running games in a set world but I would have to have time to read up on that world first. When running the game, I generally go easy on the lower level groups and will actively try to kill groups that are epic level (though they is also a way to 'beat' every battle). I generally try to do an even mix of combat and roleplaying will usually alternate combat and roleplaying weeks in the campaign. I've ran campaigns that brought players from low to epic level that lasted years and I've ran games that lasted only a session and I like them all. My world is very story based and does require players to actively know what is going on in the world though the world is basic enough where they should never have to read a paragraph or two to get the basic feel of the world and more information can always be supplied if their character wants more knowledge. I'm also always open to player suggestions and shape the game according to what the players want.