St Augustine beach is about a 1 hr & 45 minute to 2 hrs & 15 minute drive depending on how fast you drive. you go east on I-4 then north on 95. once you get to 95 N it is about an hours drive. St Augustine is the "oldest city in Florida" and theres lots of history type stuff to do & a clean beach, horse drawn carriage rides & of course local seafood restaurants & shops. I dont know anything about Cocoa Beach but wanted to clarify the location of St Augustine as it is not at the most southern tip of FL.