A.C.
Mercer Arboretum is east of I-45 off of 1960. It is full of trails and gardens with plenty to leek at for kids and adults.
Lake Houston Park is off of 59 and has lots of nice, wide sandy trails...also plenty of shallow water for wading.
http://www.houstontx.gov/parks/lakehoustonpark.html
Here is the link for the Texas State Parks systems. You can search by region and find something close to you. You are going to have to drive for just about whereever you choose, but we have some great parks.
http://www.tpwd.state.tx.us/