S.T.
I grew up in League City.
Area parks: there is one by the train station on HWY 3 and 518 in "Old" League City. my girls enjoy running around there. There's two parks with walking trails:
Countryside Park on Bay Area between 518 and 528. Coming from 518 it's on your right.
Challenger Park on 528. If you take 45 north exit NASA and go left under the freeway. You'll pass Burlington and keep going a bit. The park is on your left and I believe there's a brown parks dept street sign on your right letting you know where it is.
Have you been to the boardwalk in Kemah yet?
There's also Bay Area park and Frankie Carter Randolph Park and Armand Bayou Nature center (I'm sure you can find all these online.)
S. in Alvin, mom to four girls