There's plenty to do and see on Nevis. Go to www.nevis1.com and you'll find tons of information. After reading the material there you should be able to decide if you want to take a day trip (very easy from St. Kitts) or spend a few days on the island. Personally, if you are only going to spend only a week for your vacation you'd be better off staying on either island and going to the other one for a day trip. On the other hand, if you are going for 10 days, you could have the best of both islands and easily split your time equally between the two. The choice is really yours.
Both islands have plenty of attractive beaches but you should know that there is very little "walk-in" snorkeling on either island. Compared to places like the USVI's, the BVI's, the Tobago Cays snorkeling around both Nevis and St. Kitts is just average at best.
Now, if you take an organized day sail from St. Kitts you'll go over to Pinney's Beach on Nevis where you'll have lunch. Usually on the way over (but sometimes on the way back) you'll stop for snorkeling at Shitten Bay (off of St. Kitts) - it's the best snorkeling in the area (but it's not great). If you decide to do a boat trip while based in Nevis it will be a 1/2 sail to Shitten Bay for snorkeling.
Weather and seas permitting you could, if you want, charter a sail boat for the day and circumvent Nevis but it will cost you $600 to $800US. FYI - St. Kitts is too big to circumvent in a single day. Your other boating option on either island is to go Deep Sea Fishing - depending on the size of the boat a half day charter will run you around $500 to $600US and a full day will run $1,000 to $1,200.
You might want to split your visit between the two islands. They do have a different atmosphere, Nevis being the quieter, less busy island.
If you have 10 days, i'd split it 5/5 or 4/6 ending up in St. Kitts for your flight home.
For snorkel trips in St. Kitts, I've always liked Leeward Island Charters, which follow the route mentioned by CaribSurfer.
One alternative on Nevis is the Star. You can sail on a half day or whole day, with snorkeling at Shitten Bay (same as all the other charters) but you're with only a few people. Their website is: http://www.starmonkeys.com/Home_Page.html
We've done both trips a couple of times and have enjoyed both the larger and smaller tour.
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