M.K.
St. Paul Public Libraries have passes to the Children's Museum (they're called Passport to play) for free. Awesome children's play area!!
Also for library story time, visit this sight for times, locations, and sign up information http://www.hclib.org/BirthTo6/Storytimes.cfm
The Hopkins library and St. Louis Park have fun toy play time after stories are done. Also, the SLP one requires no sign-up!
Edinborough park has a climbing gym (but lots of it is kin of big for toddlers), gym with balls, and a jumparoo. Season passes are $100 per year or $5.50 per visit. Kind of spendy.
Also, Chaska Community Center has a great pool area for kids, but again really spendy for season passes or daily. They also have a toddler play area.