If you happen to go to the Mall, it is open before 10 for Mall walkers-- you can see the inside, etc. etc., you just can't buy anything.
There is a 24 hour IHOP across the street from the Mall so considering your early arrival hour, maybe you can stop there for breakfast first. The IHOP has free wifi internet.
If you head in the direction of downtown, there is a 24 hour Walgreens at the 46th St. station, although that may not be very exciting.

A Burger King is up the street, between 46th St. and 50th St., so you can maybe grab breakfast there and go on to Minnehaha Park and Falls. A train ticket is good for 2 1/2 hours of unlimited travel, so you can get off at 50th St. or 46th St., see the park for a short time, then continue to somewhere else. The draw of Minnehaha Park is a waterfall which is a 3 min. walk from the 50th St. station platform.
As for other stations, there's not much to see or do at the Ft. Snelling, VA Hospital, or 38th St. stations. Lake St. has a number of businesses, but is of limited tourist interest (unless you want to go to a 24 hour grocery store). Franklin doesn't have much either. The West Bank station is about a 10 min. walk from the edge of the Univ. of Minnesota campus, but the area within 4 blocks of the station is a little bit shady. between the West Bank and the end of the line, Nicollet probably is your best bet. Hennepin (literally 1 block from Nicollet) is more lively at night, but will be quiet dueing the day.
If you have any specific questions, PM me to bring my attention back to the thread. Minneapolis, and more specifically "Hiawathaland" (the area immediately around the light rail line) is my old stomping ground, having lived there all of my youth, and returning a few times a year (on long, intentional NW connections

).
Have fun!