Northwest Hills generally feeds into Doss... The neighborhoods that feed into Hill are parts of Jester, Great Hills, Westover Hills, and a couple others.
I don't know of too many high end apartments around there but there's a fair amount of nice duplex's in that area that might suit your needs.
Of the complexes I know, I can't specifically remember names but I know their locations.
-Treehouses/Treehouse or something (The entrance to them is at the bottom of the Spicewood Springs hill, just to the left at the bottom on Adirondack.)
-There's some near Jester around 2222&360 (you can see them up on the hill)
-There's a complex directly across from the Treehouse one's. You keep going down the Spicewood Springs hill, across 360 (the road changes names when you cross 360) and it's your first right after you cross 360. At the end is the complex.
I'm not 100% all of these go to Hill but just the ones I can think off the top of my head.
To go to Hill, there aren't too many complexes. You might look around to rent a duplex. I lived in a duplex off Mesa almost across the street from Anderson High for 2.5 years with 2 of my buddies. Our half was 1 car garage + 3 bedrooms/2 bath. Loved it. Rent was cheaper than what I paid in an apt.
i rented a house on highland hills blvd a few years ago for about $1500/mo. that was a 3/2, ~2000+ sq ft, big deck, and a small pool. you might consider going that route as well.
Le Montreaux
I have never been in one of the units but it appears reasonable from the street.
As others have said, there are a number of nice duplexes and townhomes for lease in this area.
Interesting you mention Hill Elementary. My partner and I bought a duplex over here this summer. When we put the other side up for lease, one of the prospective tenants expressed interest because she wanted her kids to attend Hill Elementary. Is it supposed to be better than some of the alternatives?
i have a friend who lived in le montreux. not that great. this was a few years ago and it was getting a bit run down.
i have a friend who lived in a small apt complex off bent tree and then moved to another complex across from anderson high right next to the "mesa stop 'n go" or whatever it is called. i went to his place to hang out at both places many times. they weren't that great. the one by the mesa store didn't have washer/dryer connections in the apt either.
i would do the rent duplex/house route personally.
I am living in a duplex just a bit south of Murchison - love it...there are always lots of places with for rent signs in the area too (I live on Shadow Valley). I would highly recommend that over the apt option. Oh yeah, Le Montreaux is a dump.