There's plenty of interesting things to do and see. Here are a few for starters:

1) Hike through a rain forest
2) Visit the Admiral Nelson Museum
3) Search for the ghost of Eden Brown as you explore the ruins of the Eden Brown Estate
4) Visit the Nevisian Village
5) Explore the ruins of several old sugar plantations
6) Discover the Hot Springs baths
7) Hire a guide and climb to the top of Mount Nevis
8) Visit the Botanical Gardens
9) Search for the lost village and bat caves on the slope of Mt. Nevis
10) Check out the ruins of Cottle Church
11) Take a 1/2 day sail/snorkel to Shitten Bay off of St. Kitt.
12) Go on a half day or full day deep sea fishing charter
13) Go windsurfing
14) Rent a hobie Cat for an hour or two.
15) Waterski
16) Go kayaking
17) Go scuba diving
18) Explore the ruins of Fort Charles, Fort Ashby and/or the Ramparts atop Saddle Hill
19) Check out the wood carvings of Kennedy Tyrrell.
20) Watch the sunset while drinking a Killer Bee at Sunshines or a Stinger at Chevy's.

And much more.

For a website that will tell you everything you could possibly want to know about Nevis visit:
www.nevis1.com

check out these sites:
http://www.nevisnaturally.com
http://www.geographia.com/stkitts-nevis/
http://www.geographia.com/stkitts-nevis/knpnt03.htm
http://www.travelandleisure.com/the-ultimate-caribbean/nevis.cfm
http://www.stkittsnevis.com/
also a great site, slightly biased against the Four Seasons, but thorough: http://www.nevis1.com/
A_Traveller has laid out more to do than you'll be able to cram into one trip! Ask your hotel for assistance and let them suggest a "dine-around" to the other hotels and Plantations and better restaurants. The only thing I would add is to spend a day walking around Charlestown. The CourtHouse/Library was built in 1864 and is still in use, the Jewish School and cemetery, Alexander Hamilton's Fathers warehouses - still in use - the cricket grounds... and gather a bit of local gossip at the vegetable market. Don't expect any sidewalks as the town is 400 years old. St. Thomas Anglican Church (the oldest Anglican church in the Caribbean) between Jessup's Village and Paradise. The beaches are a wonderful place to spend a few hours (with a high SPF sunblock) and tourist type shopping is almost non-existent. You have a real Caribbean experience awaiting you.

Wow, A Traveller, good going!

I wish I had your list with us when I went. Don't forget the Saturday morning market in Charlestown, great sights and smells and tastes.

You can also check out www.nevisisland.com

Thanks A Traveller for all the suggestions. I am so looking forward to this trip. I've been to most of the islands in the carribean, but never to Nevis or St. Kitts.

I'll add that you should take the ferry over to St. Kitts for the day, since it's your first visit. Take a little walk through the town, have a cold drink upstairs at the Ballahoo on the Circus (the main town square), then hire a taxi driver to give you a tour--especially visit Brimstone Hill (www.brimstonehillfortress.com).