Both previous answers are useful as far as they go. However, there are two lines passing through the 77th St & Lexington station; the already mention 6 train as well as the 4 train, so that may increase your options depending on where you are staying. With regard to bus transport, it helps to know that the M1, M2, M3 & M4 buses head Downtown along 5th Avenue. The same buses head back Uptown along Madison Avenue, so again, which buses you might use will depend on where you are staying. Also bear in mind that if you use buses, you must have the right fare in hand when you board, since I believe drivers do not dispense change. Of course, if you have an MTA card, that can be used on buses as well as the subway system.