I've been going to Sheikh Chilli's for years. (6121 Hillcroft St #N) Love their goat/chicken biryani. Strip center dive with no aesthetic allure. But good service from friendly folks. They'll answer questions, but don't expect them to go real easy on the ghee. It ain't low-cal at Sheik Chilli's.
Sheikh Chilli's Restaurant
6121 Hillcroft St, Houston, TX 77081
I nominate for best in town Himalaya, a Pakistani restaurant on 59S at Hillcroft in what is called Little India.
Both excellent; I prefer the chicken. You will find lots of mentions of Himalaya on this board and on local blogs, etc., almost all rave reviews.
Closer to where you are you might try Lazeeza on 1960W near Veterans Memorial. I haven't eaten at that one but have eaten at the one on Hillcroft. Food was good though not as good as Himalaya and I did not try the biryani.
Since you're new in town that b4-u-eat website is a good local resource for finding out what cuisines are available and where they are.