So I'll have a day in downtown Minneapolis.

Check out the Walker Sculpture Garden. It's art, but it's outside. It's close to downtown.

For shopping, you and your girlfriend can just go up into some building and get lost in the skyways. Dayton's is up there as well as many other stores.

I used to spend way too much time at Shinder's over by First Ave. I'm sure that your girlfriend may prefer some place a bit more exotic than an extended news stand, but hey.

Sex World?

I know there are a ton of veggie places in Mpls, I'm just not familiar with them.

Seems like there's a few veg eats on Hennepin. Good Thai place too where some nights they let you set your own price.

And Ember's. And Uptown. And that bookstore.

I act like I know my shit, but I haven't been there since 2000.

If you're looking for a brunch place, I love this Spanish joint called Maria's. It's located...somewhere. Cornmeal pancakes, mmmmm.

Dude, Minneapolis has one of the most exciting art galleries in America, the Walker Art Center. It has a cafe with lovely food and is near nice parks and the downtown shopping. Marshall Fields has very good sales and there is no sales tax of any kind on clothing in Minnesota. Or you can eat great Vietnamese and Mexican because of the significantly high presence of people from those places who have settled there. In the warehouse district (also good) are nice modern cuisine places like the vegetarian-friendly Cafe Brenda, New French Cafe - actually vegetarians don't have a problem at all in the Twin Cities.

seriously the best pizza i've had is there...in uptown...galactic pizza. a lot of it is organic, too. there's also this laid back veggie place called "hard times cafe" that's tasty.
do a couple of searches on places to eat & you'll usually end up near some cool places.
the walker center has a chuck close exhibit that just opened. his work (particuarly when you're able to see it 'over the years') is amazing.

If you're looking for restaurants, just walk down Eat Street and you'll find some great places:

http://www.minneapolisunwrapped.com/pages/eat_street.asp

theres a great raw food resturant called the ecopolitan (.com) thats nearby the walker

see the walker and the art musuem by the spanish dude who makes them all look like spacey whale skeleton.

SEE THE WALKER THOUGH
SEE THE MOTHERFUCKING WALKER.
NOW

there are a lot of great places on eat street (nicollet between downtown and 27th, roughly. i like a vietnamese place called Quang a lot, but there's a good real mexican place called Taco Morelo, a late night punk fake mexican place called Little Tijuana, and a passable but kind of aggravating pan-asian place called Azia. And the Black Forest, if yr into german, and there is a famous huge Avedon print with a bullethole in it hanging in the bar.

maria's is not too far from everything else, franklin and... grand? i don't remember. yeah, good pancakes.

agreed, go to the walker. very much the beaten path but that's for a reason. hanging out in the adjacent sculpture garden is pretty cool too. pack a lunch from somewhere (if it's not a billion degrees) and spend a few hours.

the hard times (famous for, among other things, booing winona ryder when dave pirner brought her there) has some pretty good food but i don't like hanging out there frankly. around the corner from it is a place called the Wienery (three guesses what they sell there).

across the river to the NE from downtown is the University area. the U has a big gehry building on its campus which is worth a look, but there's not much else over there.

if you're in town on a sunday and you want to play some kickball, there's a standing pickup game at 1pm that i do in a park off Franklin north of lake of the isles. come on down!

Maria's is on 11th and Franklin, I think. If you go east on Franklin, the Seward Cafe also has veggie/vegan breakfast & lunch.

'chef e's soul food' on nicollet...try the blackened catfish, mac/cheese and fried green tomatoes. finish up with a slice of buttermilk pie. you shan't regret it.

i completely skipped the bit where you said "vegetarian." forget the Black Forest and the Wienery but the rest should be ok.