I did a quick search on our MLS database for lease houses showing either Westwood HS or McNeil HS as the assigned schools.
I looked for 3 bdrm/2 ba homes that allowed pets. I found 72 houses or townhomes available for rent. If you have no pets, there were an additional 10+ options shown.
27 housing options for Westwood HS ranged from $895 for a 3 bdrm/2 ba, 1,616 Sq.Ft. Townhouse to $3,150 for a 4 bdrm/3.5 ba, 4,100 Sq.Ft. house.
45 housing options for McNeil HS ranged from $1,000 for a 3 bdrm/2 ba, 1,381 Sq.Ft. house to $1,995 for a 4 bdrm/ 2.5 ba, 2,726 Sq.Ft. house. [But there is a 5 bdrm/3.5 ba, 3,169 Sq.Ft. for $1,850 in Avery Ranch which may offer you more "bang for your buck")
As you probably know, Westlake HS is not in RRISD, but EanesISD. With the same criteria (3 bdrm/2 ba, allowing pets)I found 47 housing options showing as available with Westlake HS as the assigned HS. If you have no pets, there are an additional 12 housing options. These ranged from $1,100 for a 3 bdrm/2 ba, 999 Sq.Ft. condo to $12,000 for a 4 bdrm/4.5 ba, 3,686 Sq.Ft. house. I found 12 available housing options for Westlake HS for $2,000 or less.
If you decide that you would like some local expert help in locating your new home in Austin, I think you see that there real estate professionals ready, willing and able to provide accurate information and make your move to Austin easier and less stressful.