Yes, South Lawrence, especially the Mount Vernon neighborhood abutting Andover is the nicest neighborhood in the city. Basically the closer you are to Andover/North Andover, the nicer it gets. This doesn't mean you won't have the general city atmosphere but it's definitely not the ghetto.

If you're not tied to a specific area and are comfortable with the commute, I'd suggest looking in Salem, NH and the surrounding areas. Real estate tends to be cheaper in NH. Might be worth it for a little more peace and quiet. Even check out Haverhill.