The Crystal Court in the IDS Center, at 8th and Nicollet, is somewhat of a landmark - a big, open indoor space.  From there, go across the street to the Wells Fargo building; there's a nice display of art deco glass on the first floor and, I believe, the second.   The Gaviidae Plaza, which is the indoor stretch between Saks and Nieman's (which I believe is closed) is not a half bad place to shop.  Solera, on Hennepin & Ninth, has pretty good tapas.  But for a real blast, go to the Chambers Hotel, across from Solera, also on Hennepin and Ninth.  It was built by a local art collector, Ralph Burnet, and includes a gallery, video art in the hallways, graffiti in the stairwells by local graffiti artists, and lots of interesting and offbeat works of art.  Down the street from there, at Ninth and Marquette (just down from Hell's Kitchen) is the W hotel, in the old Foshay Tower, which is an interesting walk thru and also a Burnet property.  If you have a bit of free time, rent a bike from one of the rental bike racks and pedal yourself over to the Walker Art Center, which is one of the best museums for modern and contemporary art in the country, and that has an unparalleled sculpture garden.  There are lots of venues for local music - First Avenue, at First Avenue and Seventh Street, is notable.  Have fun!

I would definitely go to 123eatery for dinner but it does require reservations at least 1 day in advance.  There is a cupcake place just the north of Nieman Marcus.  

I no longer receive PM but good luck there a lot of other intersting places in downtown.

If you like hells kitchen stop by devils advocate on 9th st & Marquette they have tons of different beer to sample & their happy hour is great
I also like Haute dish & Monte Carlo.
Definitely agree on the walker & sculpture garden.

A new place opened by the Eagle bolt bar on Washington called the Zen box.
If I'm looking for something to do & not want to search too much I go to secrets of the city website they have all kinds of info.
Enjoy your stay

Google these things if you are interested

Walker Art Center (already recommended, the art center itself you have to pay for, the sculpture garden just north of the center is free!)
Stone Arch Bridge
Lake Calhoun (recommend bike/walk/jog around, and there is a food place on the north east corner of the lake if you get hungry)
Downtown walking: Nicollett Mall, Hennepin Ave, and the River Walk that goes along the Mississippi on both sides.
Disc golf! But you'd probably need a partner with discs. If you have this, Wabun near Minnehaha park or Highland Park in St Paul are both good beginner courses.
If you're biking, there are plenty of green-ways that are for bikes and pedestrians only.

Enjoy your stay!

I live in downtown and love it here. Pizza Lucé on 4th between 1st and 2nd Ave is great for a slice, a whole pie, or pasta etc, also has a full bar which is sometimes a good hangout. Dancing Ganesha at the corner of 11th and Harmon is great Indian food with a modern relaxed atmosphere. Stone Arch bridge and the walking/bike paths along the river are not to be missed. Rent a bike from One on One (on Washington between 1st and 2nd) and you'll be set.