Hi Lindsay, It's great that you're looking to move to Middle Tennessee. Nolensville borders Brentwood, but it's a little further East. In the middle of Brentwood and Franklin you have access to Interstate 65, which will take you into the heart of Nashville when going North. In the middle of Franklin right along I-65, you have the Cool Springs area which has just about every shop and restaurant you can think of. Franklin also has the historic Downtown area, which offers more local-charm. Part of Cool Springs is technically in Brentwood, but there is a small downtown area in Brentwood as well that has a decent selection of shopping, restaurants and activities. Brentwood and Franklin are also quite sizable business districts (Brentwood is HQ to many companies including Tractor Supply, LifePoint Hospitals, etc. with Franklin being HQ to Nissan North America, Community Health Systems and a host of others.)
Nolensville is growing and has quite a few new developments, but it doesn't contain the business and commerce like Brentwood and Franklin. If your neighborhood is near the newer section of Nolensville, you'll have access to a small handful of restaurants, a couple of grocery stores and a handful of shops. Nolensville is a little removed from Interstate access, but depending on where you are might get you closer to I-24. So I would consider much Nolensville to be country living within an actual neighborhood community.
You do have the shared Williamson County schools in most of Nolensville with Brentwood and Franklin. Although you need to check the county for each area separately as there are parts in Davidson County as well. For the most part, you will be able to get more house for your money in Nolensville, but the home prices are becoming a little more competitive.