Ubering from airport advice

Sorry for the weird question, but honestly would love some help for a broke dude. I am flying in for an interview into IAH around midnight on August 11th. My interview is downtown. Obviously, I'm not gonna find a downtown hotel with a free shuttle that will come get me at IAH so I'd have to Uber there at midnight which I'm assuming is expensive. So my alternative is getting a cheaper hotel by the airport with a free shuttle, then ubering Monday morning to get to the interview around 8:30, which will potentially be expensive also, maybe cancelling out the money I'd save the night before. Any thoughts or advice? Thank you!