Ha ha! I am the same way - I ALWAYS scope out the libraries!
I second the vote for the Central branch of the Lexington library (on Main St). It includes a great art gallery (currently featuring a craftsman/bungalow exhibit with some great examples from surrounding neighborhoods), an organic cafe and coffee shop, large theatre that features both stage productions and films, a great used book store in the lower floor, and a unique pendulum that swings from the top of the five-story atrium (a science exhibit itself!).
Plus, it has a great location - on Saturday mornings you just walk across Pheonix Park, with its fountains, trees, and benches, and you are right in the midst of the Lexington Farmer's Market, which has some fabulous local items and street musicians. It is a great place to really get a feel for what the downtown area offers. Plus, use their parking garage and get your ticket validated for three free hours.
Other suburban libraries are nice, but pretty standard. Most are in modern buildings. If you're looking at the Beaumont neighborhood, the Beaumont branch is right near the entrance along Harrodsburg Rd. An interesting branch is the Village branch. It is in the Cardinal Valley area of Versailles Rd, which has a large and growing Hispanic population. It is a small branch, tucked into an unassuming storefront, but it provides such a unique environment to serve its community. All of the staff are required to be bilingual, and in fact almost all are native Spanish speakers. Materials and programming are offered in English and Spanish. It is really a vibrant library with a great sense of community - one of the most unique I've experienced.
For more info on the Lexington system, see
http://www.lexpublib.org