Well it sounds like you are just south off 288 between loop 610 and the Beltway just past Reliant Stadium. Your best bet is Memorial Park Tennis Ctr with 20 courts or Lee LaClear with 26 courts. Very easy to get games and join leagues......etc. Both also have stringers who do good jobs, if you check out Mermorial ask for the manager Eric Youmans top Texas player and played at Houston when they had top 5 program back in the 70s. He can help set u up and is awesome guy.
If you want private check out the Downtown MET just off Smith (west side of downtown) that has like 20 indoor courts, can't miss the place as it's on the top Smith St garage next to the ChevronTexaco heritage building.
As for shops the closest would be the very large one on Westheimer and Wilcrest just west of the Beltway they have everything you need and top stringers.