You would use "a" to express a general destination, or plan to go somewhere: Todos los años vamos a Florida. El año que viene vamos a veranear en España. ¿A dónde va este tren?
"Para" is used for more immediate and permanent destinations, and concentrates on the destination rather than the going. So saying "A las cinco (me) voy para la casa" is almost like saying "At five I'll be home." If you don't like your seats in a movie, you can say "Vamos para el otro lado" meaning that you'd rather be on the other side. So when you use "para," especially with the reflexive "irse", it's more about changing locations than going somewhere. If you're studying with your friend's house and it becomes to noisy, he can suggest "vámonos mejor para la biblioteca a estudiar." If a man get put out of the house by his wife, you ask "¿Para dónde irás ahora? which is like asking "Where will you live now?"
Another little nuance of "para" is that you use it when you're already on your way somewhere. So if you say "este tren va a Madrid" it means that this train generally goes to Madrid. However "este tren va para Madrid" means that a specific train is about to leave for Madrid.