Most places on campus can be reached in a short walk.
The city bus system offers free fares to students, but nobody has every actually seen any Kentucky students on a bus that runs anywhere but campus. Most people seem to enjoy the walk, unless the weather is bad and the buses crowd up.
Cabs in Lexington aren't too expensive and are the best way to get where you want to go safely without having to walk. Always keep the name of a good cab company handy when going out just in case your designated driver decides to be irresponsible.