I'd recommend the following:
Key's Cafe (at the Foshay on 9th St)
Peter's Grille (I think its open until 7 PM and they offer nightly specials for very low prices (Ribs and Chicken noodle soup, etc...): Peter's is more of a lunch place, so it probably won't be very busy.
Bombay Bistro: Marquette between 8th & 9th: Indian food
Ike's on 6th Street: Its more of a bar, but they serve great burgers
Glueks (6th St between Hennepin & 1st Ave): another bar, but they have great sandwiches, burgers, plus a nice beer hall atmosphere
McCormick & Schmicks (Nicollet & 9th St): Has two happy hours with very inexpensive burgers (around $2.00 - $2.50) as long as you buy a drink
Macy's: Although you mentioned dinner, if you're ever downtown for lunch I'd highly recommend that you check out the Skyroom on the 12th floor--which has a great salad bar (plus soups) and a decent view overlooking downtown
One site to check is the
www.downtownjournal.com which has a section on happy hour specials in dt Mpls
Although outside of downtown, I'd also recommend Pizza Nea and Punch over on East Hennepin (the current issue of the DT Journal has a $10 off coupon for Punch).