Hi Misa, I'm originally from MN (all of my family still lives in the Twin Cities area--mostly on the E/NE side) and we visit a couple of times a year. While I can't recommend hospitals/peds, there are a few places we always enjoy visiting. They've got a great assortment of museums in the Twin Cities, many of which are in St. Paul! They have a great Children's Museum and Science Museum. In Mpls, there is a very fun art museum with great outdoor displays that are fun to visit in the summer. Como Park, in St. Paul, has a free zoo and wonderful grounds to wander--paddle boats for the summer and cross-country ski trails in the winter. Way south of the Twin Cities is the MN Zoo, which is enormous, but well worth a visit or two. There is a very vibrant family scene there--the Winter Carnival is fantastic! Ice sculptures and parades and all sorts of festivals involved. If you enjoy outdoors activities and state parks, it is well worth it to get an (inexpensive) parks pass that admits you all year. There are state parks EVERYWHERE. They have Trader Joe's and Ikea (my kids love that place, too). Those are the big things that come to mind for me. Like I said, the family scene there is very big and there are activities and festivals nearly all year round. If you ever go to Mothering.com, check out the "Finding My Tribe" area for MN/Twin Cities and search the threads there, or post for more family info and I'm sure you'll get good responses.
Oh, I just remembered, too, that one of my favorite kid/baby stores is located in St. Paul, too:
www.peapods.com They have cloth diapers, baby carriers, natural toys and clothes. It pretty much rocks! While the weather there will be colder and more gray, I'd say it is made up for by all the things to do. Have a safe move!