How to spend a morning in Houston before going to IAH?

I'm flying into Houston on Tuesday evening and getting a flight out of IAH on Wednesday at 4pm. I'm thinking of doing the Space Center VIP tour 9-12, get a Lyft/Uber to IAH at 1230 ish, hopefully be there 130. I've seen a few old posts asking similar questions about whether they can walk around all of the space center in a half day, and it sounds like Houston traffic can be bad, but is finishing a fixed tour like this almost 4 hours before take off still a terrible idea? Any alternatives anyone would recommend to the space center otherwise? Haven't booked a hotel yet, was thinking of downtown. Thanks!