If you do plan to go out on saturday you can take a stroll down ocean drive or visit one of the many restaurants on Lincoln Rd. which are all open till late. If you prefer loud music and a lot of other tourists around you Ocean Drive would be the best place to go, however if you prefer a bit more quiet area and want to enjoy the ultimate "people watching" experience you'd better go to Lincoln Rd.
After a hard night of partying you want to go for a late night snack, your best bet is to walk towards 15th street and locate "Five guys, burgers and fries". These guys will surely tame any midnight munchies you might have. If you feel like the burgers are to small, cross the street and head-in to Cheeseburger Babies, their 1 pound 100% pure angus beef burgers will suffice for even the hungriest among us.
These are some good options when going out on a Saturday night in Miami Beach, but like mentioned before, if you want to go out and really party you'd better wait for a week day as that's when all the night-crawlers really come out.