you will pay the same as a whole night, because you are using the room and they have to clean it the same as if you stayed all night (same goes for most hotels, unless you know someone there who will let you in to use the lobby or something). this is pretty hard and fast with most hotels. zaza is particularly persnickety about shooting on their property if you are not having an event there (unless you just want to shoot IN the room). icon and magnolia and alden are a little nicer, if you are renting a room you can shoot in their hotel as long as you aren't being obnoxious about it and let people know what's up.
rice hotel isn't a hotel, it's a residence that used to be a hotel. you would have to speak to the catering manager (sambuca catering) to use the ballroom or empire room... not sure if they would be available depending on their event schedule.
rice university is a good option, but you will need to register and pay a $50 fee to use the campus, and you're limited to certain areas. the halls where you can shoot are not indoors, but they are covered. i've shot there in pouring rain before (luckily he rain started after we got there). if your photographer knows what they're doing, though, a lot can be accompllished.
if you MUST be indoors, and you want pretty guaranteed space to shoot in, you're going to have to pay for it.
what kind of pics is it for? for people in regular clothes you have a lot more options than if it's for bridals or boudoirs or something.