Chicken Fried Steak (if they're thin enough that is) with oodles of brown gravy and caramelized onions, a huge scoop of rice under it all and maybe some sort of dark leafy green on the side to at least look health-ful, sounds good to me
I buy eye of round quite often. I use it in stews (Norwegian Sailor Stew comes to mind, as does the venison-ale stew I make--I think I've posted both recipes and Whiskadoodle tweaked the Norwegian Sailor Stew recipe)--both of these stews contain beer/ale. You could marinate the meat overnight in a marinade containing beer, wine, or brandy. You could also marinate the meat in black tea to tenderize it.
With homemade beef stock it is fantastic. I think my recipe is in one of the Bon Appetit cookbooks I have, but this sounds identical, except the title was Braised Beef with Orange or something like that. I have used round steak with the fat removed, can't think why eye of round wouldn't work.