Saipan has some amazing spots and activities not always visited/experienced its by visitors. Click on the links for more information on the particular sites and activities.
Snorkeling & Swimming:
Managaha Island, Pau Pau Beach and Wing Beach are probably the easiest places to snorkel without having to go outside the reef. For the more adventurous snorkeler, try the Boyscout beaches.
Managaha Island: One of the most popular sites on island. Amazing beaches with some of the best snorkeling on Saipan.
The nicest sandy beaches are probably Managaha Island, Micro Beach in front of the Hyatt, and the beach just South of Sugar Dock.
No visit to Saipan would be complete without having tried outrigger canoeing. There are 3 canoe clubs on island; Saipan Fatuul, Napu, and Saipan Outrigger Canoe Club, contact them and they'd be more than willing to show you the finer points of paddling.
Mt. Tapochau: See the whole island from the top of Mt. Tapochau
The best way to see some of the more hidden places of Saipan is by hiking. As of right now there are no established hiking trails so having a local show you around would be your best option. Another good way to get of the beaten path is to run the hash. The Saipan Hash House Harriers meet every Saturday (3:30 or 4 pm) at the bank of Guam in Garapan.
Forbidden Island: One of my favorite spots on the island. A 15 min hike along a trail takes you down to a deserted beach with a swimming hole and a hidden pool inside a cave.