...Also, go to the restaurant on the water. I think it is called the Pier as you walk down a long pier to get to it. Try the lobster bisque...
FYI, that restaurant is called the Boardwalk, and yes, the lobster bisque is pretty good. I almost always get a bowl when I visit there.
The only "must do" that I can think of, is to go to several of the bars. The Beer Barrel, as previously mentioned, has the world's longest bar, and you should watch Pat Dailey if he's playing that evening. During the afternoon, we usually go see Mad Dog over at the Round House and order a few buckets of beer. It's the smallest bar, but often has the best afternoon atmosphere. You might also want to order a pizza at Frosty's. It's not the best pizza, and like most everything else on the Island it's a bit pricey, but it's another fun stop that regulars like to visit.
PIB can be a lot of fun, but make sure that you don't walk around the street with any open containers, or you'll be slapped with a fine in excess of $125. That makes for a very expensive beer.
If you don't ride over on the Jet Express (aka the pricey ferry boat) then you will arrive on the back side of the island. Then you'll need to catch a bus (only a $1 - $2 per person) to get to the main area. If you enjoy walking, then you can save the bus fare and hike the 1.5 miles or so (it's longer than it seems, trust me). Also, the cheap ferry (Miller Boat Line) has their last boats leave the island around 8:30 or so, so it's not the best choice for people that want to party later.
One thing my wife and I did with one of my brothers that was pretty fun, we took a tour of the island on Segues (the two-wheel balancing scooter thingys) and that was cool. It was also expensive ($60 or $90 a person), but we all agreed it was worth doing at least once. It was a great way to see the island, especially if you've never been there before. You can also rent golfcarts to explore the island on your own.