Quintana and Surfside are no cleaner than Galveston. Though they are generally much quieter and secluded. Not all of Surfside beach is a free beach, though; be aware. And it is the nicer (if you could call it that) of the two. You just have to get through some grungy areas to get there. Freeport/Surfside are rather empty and don't have much to offer in the way of amenities. The kind of beach you're really looking for...you aren't going to find that close to Houston.
I like Surfside/Quintana. Not nearly as crowded. You can spread out and have your own space. (If you have a 4WD vehicle, especially a really high truck, you can spread out even further, but usually the closer parts are fine for any vehicle.) Some of these places don't necessarily have showers, bathhouses, etc., but you don't have to pay for them either. You can go to Lake Jackson for food, shopping, etc. if you need to.