downtown staying at Hotel Minneapolis
As a visitor to Minneapolis, my suggestions woul dbe Restaurant Alma (10 minute cab) and Bar La Grassa (also about 10 minute cab). A little further, Piccolo is about a 20 minute cab.
528 University Ave SE, Minneapolis, MN 55414
Bar La Grassa
800 N Washington Ave, Minneapolis, MN 55401
Search "Downtown" on this board, and you will get tons of recommendations. My rec right now is Saffron, which has some of the best food and cocktails in town.
If you're cabbing it, go to Heidi's, just south of Downtown. The overall dining experience there is pretty close to flawless, the food is great, and the space is awesome.
For cheap (or lunch), head to Quang for Vietnamese.
For a night cap, go to Bradstreet at the Graves. Their cocktails are simply superb.
Are you thinking lunch? bfast? dinner?
I will throw a few things out.
Breakfast (these may be controversial), Ikes- they do these sticky buns at the table as big as your head which is true cure for too many cocktails the night before. They have bloodys with everything (peperoni, cheese, shrimp, pickles, onions, olives, etc) in them and it really boasts a charm like pub or steakhouse.
But if its a good bloody you are looking for I would hit up Hells Kitchen. Neat atmosphere, and unique food. They make many things from scratch like their peanut butter and their ketchup.
Dinner: you are in the center of downtown so anything is possible really. More expensive you can trot over to Diamico at Chambers, I have had two very solid meals there recently.
Of course you have the W and you can relax in the overly crowded lounge before going upstairs to Prohibition. I have heard mixed reviews.
If you desire sushi, then Seven is really swank.
Before I continue, it would be nice to know what you are looking for... you are staying in such a central location that 5 minute cab ride can take you all over the place including northeast at Butcher Block and towards uptown at Nick and Eddies.