One afternoon/night in Houston ?

I am traveling with my teenager and will be in Houston for one night- basically land at noon and have to leave the next morning. So many downtown hotels, but its not clear that is the best location to stay. We likely just want to eat some great tex Mex and stay in a nice hotel that is walkable to a few restaurants shops etc. I ve been told midtown, but I didn't see a lot of hotels in that area. Is it dumb to stay downtown? We are heading to LA the next morning. I want to get a quick taste of Houston (we may go to cowboy museum after leaving IAH) but since I idon'thave a ton of time, want to get the best slice of Houston possible in what you can between noon and 10 pm. Safe, walkable and okay spending up to 200 per night. Any suggestions much appreciated!