I'm in Pearland (work in TMC) and haven't really left the house except to go grocery shopping since last March. I'm not altogether sure what's open and what's not.
Just be aware that Houston is HUGE. We joke that Houston is an hour from itself. But it's not really a joke. The Woodlands is an hour from downtown.
The zoo has been open, as well as Space Center Houston. If it's open, get lunch at The Dunlavy and take a walk along the bayou. The Tolerance sculptures are a nice walk from there. The Museum of Fine Arts, Houston just expanded. I haven't been to the new building yet.
There are lots of great places to eat. If they're open, I recommend Pondicherri, Hu's Cooking, Xochi (upscale), and Mala Sichuan.
If you make your way to Chinatown Star Ice and Teriyaki is fantastic for authentic Taiwanese food. Shanghai Restaurant (next door to H Mart) has authentic Hong Kong style dim sum. And on weekends Kim Son has fabulous dim sum with the trolleys.