I'll be the first to admit that this list is not exhaustive.
Here are some of the places that I love to go to for shopping and just all around walking around.
All are amazing. I especially love the Turkish grocery, Acacia and the Indian grocery, Subralaxhmi Grocers.
For everything Mexican, I go to one of the new El Rancho Markets (they're all over town) or to the Mi Tienda (H.E.B.) or to Airline Drive to the places around Canino's Market including Granel Spice Market and El Bolillo Bakery.
And, don't forget the food sections at the most excellent Spec's downtown on Smith Street.