I'm in Austin (actual Austin, not "suburbs 20 miles north of Austin"). Feel free to PM me with specific questions, but here's a few things to consider:
The housing and rental market are both ridiculously hot here. Case in point - we bought a home in 2012 that has doubled in value since then. Insanity.
It will be tricky to keep costs affordable for housing and be near downtown (though to your point, you're coming from CA, so it all seems less expensive from your perspective). BTW, there is a running commentary in Austin about "all the Californians moving here and running up costs", so I would be semi discrete about your status as an incoming Golden State-r. :) It's all in fun of course, but if you see a few eyerolls in response to when/why you got to Austin, don't be too surprised. The city has a lot of ambivalence about its own explosive growth and tensions between its original Texas weird identity and becoming a mini silicon valley with too many condos.
Downtown means different things to different people too - so I'm not sure if your job is literally downtown, at a swanky co-working space, etc. or is semi flexible about remote work, etc.
While Austin has some mass transportation, its not known for its excellent walkability in general. We have a commuter train running North/South into downtown, and a bus system that most people will say is not terrible but not super fast or efficient (given traffic). There are bike lanes in most parts of residential Austin neighborhoods (within 5 miles of downtown), but the lanes don't necessarily continue into downtown. Drivers are accustomed to seeing bikes though, so that's a plus. We have recently been taken over by all things Electronic Scooter/ Electronic Bike/ Electronic Magic Carpet Ride, etc rentals (aka, Bird, Lime, etc.). Some of these are not allowed in certain parts of downtown, esp during events like SXSW.
I think having a car is likely necessary for most people. IE, downtown grocery options and dining are going to be overpriced, etc. We're lucky enough to live ~3 miles from downtown, within a mile of my spouse's job and child's school, and I work from home. But we still use cars regularly to get across town. People do complain about the traffic, though I'm sure its no worse than CA. Still, commuting for work can be terrible, especially if you're having to go North-South on either I-35 or Mopac (also called Loop 1) -- these are the two major N/S arteries and get appropriately full of commuters between 8 - 10am, 4 - 6pm. If you can situate yourself East or West of downtown and plan to get to your job laterally, it will be much less painful for you. While you'll run across ample stoplights, it won't be quite as mind numbing.
Like many cities, Austin has been historically segregated with wealthy Whites living West of downtown, towards the hills/lakes, and Blacks/Hispanics have lived East of downtown. There is still much socioeconomic division within the city, but the East side, for better or worse, has gentrified considerably and is now full of new condos, trendy eateries, etc sitting right alongside original residents (who in many cases, can't continue to afford living in the city). This means that, in big sweeping terms, the East side is generally less expensive than the West, and more diverse. The city has super interesting demographic data that also shows more conservationism in the West and more liberal politics East, etc.
There are ample funky/cute back houses for rent all around the residential neighborhoods which may cost less than a new build condo/apartment.
It sounds like you're moving here without a family, so schools aren't a consideration, is that correct?