I stayed in St. Paul for a conference and I stayed at the St. Paul Hotel,, it's not that "budget", but it was nice, historical and I really enjoyed it.
The only ones I know you can walk to the light rail would be ones downtown minneapolis, or right by the mall of america in bloomington. Depending on why you want to be by the light rail, there are also a lot of hotels that have free shuttles to the mall of america which the light rail has a station in.
My husband just stayed at the full service Marriott, in the out lot of the Mall of America. He paid less than $100 a night, and said the staff was very nice.
There are many hotels around the Mall of America that is also near the light rail. There is a waterpark near Mall of America that I think is connected to a hotel. On better bidding you can get the hotels and their amenities and some ideas to bid on priceline. You can also go to Trip Advisor for reviews of hotels. Have a good time. Bring your winter wear though. The temps can drop pretty low in 24 hours.
I'd also try around Mall of America. There are a bunch of hotels there, including a Fairfield Inn. I have only stayed at the full service Marriott, but there is also a Courtyard Marriott nearby.
With a pool & budget I agree with pp MOA would be the place to stay. Any hotels in downtown with a pool are very nice, but aren't very budget friendly.
Jen
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