Westover Hills Apartments For Rent . Find apartments for rent in westover hills, san antonio, tx by bedroom, cheap to luxury, pet friendly, with utilities included and more. 439 apartments rental listings are currently available. Vantage at Westover Hills Apartments for Rent in San Antonio, TX from www.vantageatwestoverhills.com Located near san antonio's finest attractions. (25 reviews) food & drink. The average home rent in this residential area is $1,977.