Where to stay between NRG and Galveston?

Hello! Coming to Houston for the first time and will be attending the rodeo on a Friday night, staying in Houston area, and heading to Galveston in the morning. We plan on using a park and ride for the rodeo and will have a car. What would be the best area to stay in after the rodeo? Somewhere safe maybe on the way to Galveston but not too far from NRG? We have 2 kids. Thanks!