Palmdale is a great place for families and there are many quality neighborhoods. You will probably read many posts online about the superiority of the West side of Palmdale over the East side, in terms of school performance, crime rates etc. Since I live and work in the Antelope Valley, I can assure you that there are affordable and safe neighborhoods on both sides of Palmdale, but the best neighborhood for your family can be narrowed down based on some of your specific personal criteria.
Having a knowledgeable local agent to help with your search is a good first step towards this goal. This includes someone who will listen to your family's needs, wants and financial situation before making suggestions as to neighborhoods of interest.
In regards to your price scenario of $80K, it is difficult to find a home in any part of Palmdale or Lancaster within that limit right now. Even a year ago that limit was difficult, but it is even harder now due to the lack of supply and the upward trend in prices and interest rates. In quality areas of East Palmdale, there are few homes under $125,000 and in West Palmdale there are few under $175,000.
On the up side, interest rates are still as low as 4.5%, which is AWESOME if you are speaking historically. Now is a great time to buy, but it is hard to find a DEAL. There are things you can do as a buyer to make your chances of landing a house better, but you have to fight for the house you want.
If the upward price of homes has priced you out of the market, you can always rent for 6 months to a year to see if homes become more affordable. This will also allow you to get to know your preferred parts of Palmdale first hand. I can recommend some nice apartment communities or homes that are for rent in Palmdale if that is helpful.
Should you wish to ask further questions about the local market or your situation, feel free to contact me at the number below. Thanks for your time and have a great day!