M.F.
There are a few coffee shops that I am aware of that offer kids space and adult space.
Java Train
Sovereign grounds
You could also check out the REd Balloon for Toddler story time
Other malls like Maplewood and maybe Roseville mall have play areas as well.
Toddler Tuesday at MOA
Lookout Ridge in Woodbury (indoor play area)
Inver Grove Heights Community center has an indoor water park