Looking for a newer, safe neighborhood with reasonable rents and amenities close by? (Austin: rentals)

[uhuher]

I am currently living in Oregon, and have been watching the state's economy crash. I lived for a brief time in North Austin in the summer of 2003 and loved it. I was 23 and lived with my mother, so money wasn't a huge worry of mine at the time. Now, I have a daughter who is almost 2 as well as a fiancee, and we all live with my mother, who is nearing retirement age. We are all originally from the Seattle area of WA, and decided to move to Oregon to escape the constant rain and rising rents in WA. Big Mistake. Oregon is one of the three worst states to live in right now insofar as the economy is concerned. My mother and I would love to return to the Austin area, as we loved the weather, and all the shopping excitement a woman could want, as well as the friendly people. My fiancee is 25 and wants to get into college. My mother has many years experience in the clerical administrative field, and I am a stay at home mom, who would at some point like to go to college myself.
My concerns and questions are mainly about where exactly in Austin proper to relocate to. What we would like is to find a safe, newer neighborhood with all the shopping amenities nearby. Parks are a bonus, but not a need. We would like to have the general options of the local video store, grocery, a shopping mall, (again not a need, but would be nice) post office, restaurants, etc. I would like something that has an actual neighborhood feel to it, like tree lined streets, and a feeling of enclosure around the houses. Not an area that is wide open to strip malls and feeder roads. Someplace safe is a must as I am a little neurotic as a new mommy, and being in a family with three women and one very lithe male, I would love to be in a safe place. We are looking for rentals in the price range of $1000 or less a month for a 3 bedroom. Is there such a thing now? I looked up the apts. we lived in back in 2003. What we paid $675 for then are now $1100. Wow. I can see that inflation has hit every state hard, but would love to be some place as wonderful as Austin while suffering financially.
Any advice would be wonderful, and I'd appreciate everyone's input.
Thanks!
Madeline