Relocating to Austin, need advice when to apply

Seton and St. Davids are the two main hospital systems here. I work for Seton, just started as a new graduate RN and am going through their RN Residency program that is provided for their new nurses that get hired into the Seton system. Seton is by far the more popular place to work as far as nurses are concerned, being the non-profit and magnet status, however some people love St. Davids as well.
Typically here in Austin for either system, you need to get in touch with a nurse recruiter, let them know you're interested in GN positions, and apply for a general GN opening online. Then they forward your application to the various departments you're interested in. I haven't applied anywhere that didn't handle their GNs that way. I work at Brack (the trauma center) and am learning TONS in the residency program, which is full time and paid. I'd suggest looking into that program.
As far a WHEN to apply - do it as soon as you want to! I'd start talking to recruiters sooner rather than later so you're able to get interviews in the units you like. Austin is a fairly competitive nursing market too, just to warn you. Some people got lucky and got into their first choice, but most (including me) are starting out in other units with plans to work their way into a different area eventually. The nice thing about Seton is that they hire from within first.. so if you start in acute care, for example, they are very supportive of moving you up into ER or ICU if that's where your heart is.

You will LOVE Austin.

Austin can be a difficult market for nurses- with a major university there and it being a popular city in Texas, there is a lot of competition. One thing you might look at is the surrounding communities. Sometimes it is easier to get a job in the smaller towns that are close to Austin, and with Austin traffic being what it is- the commute is sometimes about the same.