M.W.
Hi S.,
I'm not sure how far you would want to go, but I take my daughter to Como Conservatory and Zoo in Roseville. It is basically free...they ask for a donation, but you do not have to give one. The conservatory is very pretty but the zoo is the big draw for my daughter. They have lions, a tiger, giraffes, zebras, monkeys, chimps, polar bears etc.
Another free park is Teddy Bear Park in Stillwater (also a bit of a drive for you), but younger kids love it!
I hope this helps,
M.