All in all, yes Lexington is an excellent place to live. There are parts of town you definitely want to avoid living in, but that's true for any city.
I would recommend staying on the south side of Lexington when looking for houses, as the neighborhoods tend to be better. I would stay with zip codes 40503, 40513, 40514, 40515, 40517, 40509.
Neighborhoods/areas to avoid: Anything off of Versailles Rd from downtown until you get past New Circle Rd. Anything off of Russell Cave Rd until you get past the interstate, especially the Winburn and Hollowcreek neighborhoods. The Centre Parkway area. Anything northeast of 3rd street out to New Circle Rd with the exception of the Transylvania University campus. The hipsters are trying to get a foothold in that area along with Jefferson St and N. Limestone but it's not quite there yet. The area around Bryan Station Rd and Eastland Parkway. Anything off of Georgetown St.