Daytime I'd go with Chrella's suggestion and hire a car for a day and go exploring. There's some beautiful beaches on the northern and western sides of the the island and great little beachside restaurants that aren't crowded and are cheap.
Angthong National Marine Park is a day trip you can do as well, book online or any travel agent on Samui (and at your hotel if they have a tour desk)
Depending what night it is you can start it out with one of the many walking markets. Fishermans Village Friday night is the most popular as is Lamai on Sunday night.
Depending on where you're staying but a walk up or down the main beach road in Chaweng is always going to entertain. Buy a cheap cocktail from any of the number of pop bars that appear at night and keep strolling.
Ark bar as mentioned already, it's on the beach and very popular.
Monkey bar, again on the beach but smaller and not as in your face, it's a bit futher down Chaweng beach towards the southern end.
Green Mango and Club Solo, located in central Chaweng (Green Mango Soi) Both big clubs with Green Mango being the biggest on the island.
Reggae Bar, located on the western side of Chaweng Lake. A big bar playing a variety of music and very popular around midnight or so.
Q Bar, located on the hill overlooking Chaweng. You'll need to get a taxi there. Probably the most modern and expensive bar on Samui, killer views at night looking down on the twon and nightly fireworks.
Plenty to do on this fabulous island, enjoy your trip.