I guess it depends on what you mean by a great neighborhood.
You can get a house here for under $50K, and the area isn't necessarily dangerous but the schools are not where I would send my kids and the neighbors don't keep up their yards, have multiple cars that may or may not run, in their yard, etc....
If you want anything in an area where people keep up their yards, you would feel ok sending your kids to the local school, and you still want inexpensive, you would need to go over $100K and either live in a very small house with very little yard, OR live quite far out in the country areas. But, the good thing is that it CAN be done. That is one reason we moved from SoCal, so that our kids would be able to afford staying if they chose to stay in the area.
As our kids reach college age, we have even considered buying a condo/townhouse near the campus of our local Univ. for them to live in because the mortgage would be close to renting and we could use it as an investment or rent it out later. And it is still affordable! No way we could have done that at one of the local UC schools for them!