While I didn't want to do it given the climate, i think it may be possible to be carfree in Houston...but downtown might not be the best choice given the limited services.
1. I have heard that there are apartment/condo complexes with shuttle services, catering to international residents working at the medical center/energy companies who don't drive or can't drive in the U.S.--no specific leads, but I was chatting with someone awhile back who had a friend with this living arrangement.
2. The bus service has been totally revised in the last couple years. You could look into finding a neighborhood with a good bus connection to downtown (if you're usually working during regular commuting hours) that would be more walkable for things like groceries, supplementing with Uber and car rentals for other trips.
Honestly, though, what I ended up doing was going "low-car" after being carfree for a number of years on the West Coast. I have an older, paid-off car and just don't drive much--my church, work, family, home and usual errands are all pretty close together. I'm not sure I'm saving money given that housing close to work was more expensive than if I were willing to have a longer commute, but it definitely saves hours of my life and a LOT of stress. It probably depends on the job/life, but the Uber costs for all the places I need to go that aren't transit accessible would be more than what I spend on the car.
If you do it, though, tell us how!
