Lake Travis ISD serves the cities of Lakeway, Bee Cave and the surrounding areas like spicewood, bee creek, hudson bend, etc.
Eanes is going to cost more then LT most likely. LTISD has some very affordable housing on the west and north end of the district. I live in it.
Leander ISD is another one out west thats more affordable. It serves areas like steiner ranch, leander, volente, four points, etc
PM me your number, i can tell you quite a bit. i grew up out in west austin and know it well.