I've lived in the Austin area for 20+ years. I'll do my best to offer some data.
1) The Texas School for the Deaf is just south of downtown. It's a beautiful campus with some rich history and very well respected.
2) Job market in Austin is pretty hot right now, especially in tech. It's always been strong, but really seems stronger right now. Non-tech is pretty decent too as you still have everything that's not tech related that comes with a growing city. Lots of California's have migrated to Austin and it's had the nickname of "Silicon Hills" for a number of years. Perks are usually good in tech. Pay isn't bad. That doesn't mean if you're not in tech, Austin's not for you.
3) Traffic isn't the greatest. I don't think it's as bad as Dallas was, but that's my only comparison. Lots of companies are aware of that for salaried employees, so you'll often find flexible hours or things like, "everyone should be in the office between 10-3" to allow for early risers and late comers. 30 years ago, Austin made a gamble on traffic to start updating the infrastructure to go south towards the big Motorola plant, as that's where things seemed to be moving. However, with the tech influx, things started to shift north and northwest of downtown. It's taken quite a bit for the city government to turn that ship and start building that way. Hence the problems with traffic. Toll roads have been installed over the past 10 years, which helps, but they're supposedly the most expensive in Texas. Public transportation is nonexistent. It's Texas, we have lots of land so the tendency is to build out instead of up which makes public transportation difficult.
4) Housing IS expensive. You've got a town that's growing quickly and an influx of Californians who are used to MUCH higher prices driving the cost up. When looking at housing, unless you're ready to pay $800k for a 2 bed/1 bath pier and beam starter home or a $300k one bed/bath condo downtown, you'll probably be commuting from the outlying areas. Since TSD is just as few blocks of downtown, there won't be a lot of housing options close that aren't expensive. However, you'd probably be looking south or southwest of there, which isn't quite as popular as north and might be a little cheaper. Usually older homes.
5) You mentioned someplace "warmer". You'll get that here. Yesterday was a high of 79. Not typical this time of year, but not far off. Summertime, however, will be touching 100 degrees regularly. I've seen summers of high 100's or more for 90% of the summer and others that don't crack 95. Although we're not on the coast, it still get's humid which makes the heat worse. In Austin, there's really only two seasons. Summer (hot) and Fall (cool). If there is any ice, the city shuts down.
6) Regarding extra-curricular activities, if you're into music, you're in the right place. If not..... Austin's still a small town, so big shows, museums, etc. are kinda lacking. Austin doesn't have a pro sports team, so you get to pick Dallas, Houston or San Antonio to root for. Or, you could be like most of Austin and just root for the Longhorns.... Also, since it's still a small town, you can be in the country of the hills withing 30 minutes, so if hiking/outdoor activities are your thing, there are tons of options. Plus, Town Lake (actually a river) in the center of town and wonderful weather means water activities are available. While COTA and F1 are here, there's not a huge car presence, per say. Not bad, but less than what I'd think with a facility like that in town.
Oh, and cowboy boots aren't required. Austin is unique in that it's not anything like the rest of Texas. Definitely more laid back and liberal, although still Texas roots.......
-Rob