Short Term Rental for 3 or 4 months

We have moved down here for an indefinite period right now so MD Anderson can take over my wife's cancer care. She will be getting chemo in-patient at MDA for 3 to 4 days on a 3 week cycle for several cycles.

We are looking to do a short term rental in the Houston area for 3 to 4 months. I see many on Airbnb and VRBO, etc. but I have no idea which areas of town to rent in for ease of access to MDA and safety. We don't mind driving in if it's better to be further out.

We are looking for a house (not an apartment/condo) with a yard for our dog.

What areas/sections of town should we target to stay and which should we avoid?

Thanks.