Unfortunately, I really can't vouch for their burgers -- they might be awesome for all I know!

Open mic nights are a great way to get in some free entertainment, and this one, a singer-songwriter night at one of my favorite bars, The Hotel Utah, is a great way to spend a Monday night!  Admission's free, songs are free, beer's a bit higher-priced (but you still may have enough change in the cushions of your couch to afford some brew).
Cheap Bastard says Check it out!

New England-style fish joint Woodhouse Fish, Market at 14th, has dollar oysters and $3 pints (mmm...$3 pints) every Tuesday from 4:00 on - usually until about 9:00. That's many, many hours in which to imbibe the cheapness. Split a clam roll with a pal and you're in business.