Latitude Apartments off of Wurzbach and Evers allows all breeds. Hotelwise, La Quinta is very dog friendly.
The Riviera Apartments on
Pecan Valley just east of Goliad Road are fairly reasonable, require NO
pet deposit, all bills paid, free cable.
Sun Ray Apartments (now called Escapade) on Blanco accept all breeds of dogs
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http://www.meetup.com/sanaturehounds-com/messages/boards/thread/41199122
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