Hello Island Girl,
Generally speaking, Austin, and the surrounding areas are relatively safe in comparison to other similarly-sized metropolitan areas. However, we do have some horrendous traffic here. Do you know where you will be working? I would highly encourage you to look for homes that are close to your job because otherwise you will be spending a lot of time in traffic.
Depending on where you will be working there are some areas of town that are both affordable and safe. Round Rock, North West Austin, Cedar Park, and North Central Austin are some areas that come to mind. Are you looking to rent an apartment, a condo, or a house?
If you have not yet found an agent to help you, please contact me at email@example.com and we can discuss the specifics. I would be happy to help you on your home search.