When my kids were younger, we would ride our bikes through East End Park or take a long bike ride on the greenbelts. You can walk the trails at East End Park but be careful of snakes, etc. My kids also enjoyed Jesse Jones Park in Humble.
Near downtown, there's the Children's Museum, Houston Museum of Natural Science, and you could go see an Astros baseball game.
Further away is Space Center Houston, Moody Gardens, and the Schlitterbahn waterparks.
Welcome to Kingwood. You might get more suggestions if you post on the forums/message boards at www.kingwood.com
It is time for Summer League swimming. Both of your children could do it on the same team and it would be a great way to meet neighbors and children they go to school with. It isn't super competitive and lasts until the end of June. I don't think your neighborhood has their own team, so you could join any team. Trailwood Village Gators would probably be a good place to start.