I ventured through the internet with searches like "stores open Houston".
The first thing I found was a list KHOU provided of grocery stores operating in the city.
The lists includes Walmart, HEB, Sam's Club, Spec's and Kroger.
When it comes to home repair stores like Lowe's and Home Depot if you go online and look up their store locator website, you can input your location and it'll tell you which stores are open and any adjusted business hours.
If you’re in need of a pharmacy, it works the same with Walgreen’s, but not CVS.
When I went to CVS store locator it only showed the store's regular business hours but not whether they were affected by the storm.
The phone numbers are listed, so I do suggest calling before making the trip.
As for gas stations, you might be better off driving around looking for available pumps.
Valero, Exxon, and Chevron, only provided locations and phone numbers.