I am not
so familiar with the area that I can point you to
exact neighborhoods - however I do suggest you do two things - Check with the Lexington -Herald Leader - the Lexington newspaper - and also check with the chamber of commerce -
http://www.lfucg.com/ - I think both of those options will give you a good start.
You will find phone numbers and contact info - make some calls , I assure you they will be more than happy to help and guide you to an area fitting for your daughter.
Good luck on the search - and tell her welcome!
Take care -