I work right next door to the Hampton, but unfortunately don't do much drinking around here. Not sure of anything great real close. But within walking distance (3/4 mile or less) are the Warehouse District and E. 4th, as well as the areas around Progressive Field, Quicken Loans Arena and the new casino. You're actually in a great central spot.
TSP should chime in here soon, as those are all his stomping grounds. Winking Lizard on Huron is a solid sports bar with good wings. Warehouse District offers some more upscale bars/restaurants (and more clubby places I think, and the occasional shooting), and E. 4th is more high end with some fantastic restaurants (Greenhouse Tavern, Lola, Saigon, Zocalo). Corner Alley is a bar/bowling alley that is pretty nice. Flannery's Pub on Prospect is solid.
Don't really have a hole-in-the-wall place around here to recommend.
Not walkable, but probably the hottest area of late are the bars/breweries on W. 25th by the Westside Market (Great Lakes Brewery, Bier Market and Market Garden Brewery).
That's the overview, and hopefully some more locals who get out more than I do can add more specific recommendations. Personally, I like Winking Lizard, Flannery's and Market Garden.