Houston area apartments suitable for an active dog

My SO and I have been in the search for an apartment complex in the Houston area, more specifically west Houston neighborhoods within 610 loop. While we are interested in neighborhoods such Fourth Ward, Midtown, Museum District/Med Center, Montrose, Washington Avenue, River oaks, West University, we’re open to other suggestions. At the moment we’re looking into some of the high rises within these areas, but I’m wondering if that would be a good idea considering we have an Australian Shepherd who’s still a puppy. If any one you guys could recommend an area or even a particular apartment that would be good for a couple with a friendly active puppy. I’m thinking someplace near the Hermann Park or similar park would be good to take him on walks. Would you guys suggest a mid rise complex as a better alternative? I could provide more info in the comments. If there’s a better sub for this question just let me know.