There's a great online resource of a very comprehensive, weekly updated info from a magazine called St Thomas This week. Having lived there for 13 years, I know many locals including myself who use this magazine as an informative resource for all info.
http://www.st-thomas.com/week/ (it's not as gitzy and ad driven as most publications for tourists)
It'll give you official taxi rates, cruise ship schedules (more than 3 large cruise ships in, add time to your schedule for traffic slow downs and crowds all over)
Taxi/open air surrey drivers will hound you to death at the docks...both the organized ones right at the dock and the unofficial taxi's wandering at Havensite Mall right at the West Indies Co Dock (most boats come in there; if you arrive on a busy cruise ship dock- you may be onthe other side of Charlotte Amalie Harbor at Crown Bay docks in Sub Base)
You may pick up either, and they all know each other's prices...on the unofficial ones you might be able to get the price divided if you have more than one person in the vehicle.
Sapphire and Secret Harbor are on the east end of the island. Both are beautiful beaches, Sapphire more exposed to incoming weather and chop; Secret Harbor more placid and calm. Sapphire may have better snorkeling off the two reefs/jetty's.

Following are the official fares from town per St Thomas This Week.. The two cruise ship docks are within 2 miles of teh downtown, so the fares would be a good approximation of the fares fromthe docks to the east end.

Rates in BOLD are for 1 passenger to a destination. Rates in (parenthesis) are per person for 2 or more passengers to a destination.
Location Town To Airport To
Airport Terminal 4.50(4.00) - (-)
Admiral's Inn 2.50(2.50) 4.50(4.00)
American Yacht Harbor 9.00(5.00) 10.00(5.50)
Anchorage 11.00(6.50) 12.00(7.00)
Blackbeard's Castle 2.50(2.50) 5.00(3.50)
Bluebeard's Castle 2.50(2.50) 5.00(3.50)
Brewer's Bay 4.00(3.50) 3.00(2.50)
Carib Beach Hotel 4.00(3.50) 2.00(2.00)
Coki Beach 7.50(5.00) 8.50(6.00)
Compass Point 6.00(4.50) 7.50(5.00)
Coral World 7.50(5.00) 8.50(6.00)
Cowpet Bay Village 11.00(6.50) 12.00(7.00)
Crown Bay Dock 2.50(2.50) 2.50(2.50)
Drake's Seat 4.50(3.00) 6.50(4.00)
Elysian Resort 11.00(6.50) 12.00(7.00)
Emerald Beach Resort 4.00(3.50) 2.00(2.00)
Eunices Terrace Restuarant 7.50(5.00) 9.00(6.00)
Four Winds 5.50(4.00) 6.50(4.50)
Frenchman's Reef 6.00(4.00) 7.50(4.50)
Frenchtown 2.00(2.00) 4.00(4.00)
Havensight Mall 2.50(2.50) 4.50(4.00)
Hull Bay Beach 7.50(4.50) 9.00(5.00)
Island Beachcomber 4.00(3.50) 2.00(2.00)
Island View Guest House 6.00(4.50) 5.50(4.00)
Lagoon Fishing Center 6.00(4.50) 7.50(5.00)
Lindbergh Bay Beach 4.00(3.50) 2.00(2.00)
Mafolie Hotel 4.50(3.00) 5.50(4.00)
Magens Bay Beach 6.50(4.00) 8.00(5.00)
Magens Point Resort 6.00(3.50) 8.00(5.00)
Mahogany Run Golf 7.00(4.50) 8.50(6.00)
Marriott Frenchmans Reef 6.00(4.00) 7.50(4.50)
Morningstar Beach 6.00(4.00) 7.50(4.50)
Mountain Top 7.00(4.50) 8.00(5.00)
National Park Dock 9.00(5.00) 10.00(5.50)
Paradise Point 6.00(3.50) 7.00(5.00)
Paradise Point Tramway 2.50(2.50) 4.50(4.00)
Pavillions & Pools 8.50(5.50) 10.00(6.00)
Point Pleasant 7.50(5.00) 9.00(6.00)
Red Hook 9.00(5.00) 10.00(6.50)
Reichhold Center 4.50(4.00) 3.50(3.00)
Renaissance Grand Beach Resort 7.50(5.00) 9.00(6.00)
Ritz Carlton 11.00(6.50) 12.00(7.00)
St. Thomas Yacht Club 11.00(6.50) 12.00(7.00)
Sapphire Resort 8.50(5.50) 10.00(6.00)
Seaborne Seaplane 2.50(2.50) 4.50(4.00)
Secret Harbour 8.50(4.50) 10.00(6.00)
Sub Base 3.00(2.00) 2.50(2.00)
Tillet Gardens 5.50(4.00) 6.50(4.50)
TuTu Park Mall 5.50(4.00) 6.50(4.50)
Univ of VI 4.00(3.50) 3.00(2.50)
Vessup Bay 8.50(4.50) 10.00(6.00)
Watergate Villas 7.50(5.00) 8.50(5.50)
West Indian Co. Dock 2.50(2.50) 4.50(4.00)
Wheatley Shopping Plaza 2.50(2.50) 5.00(4.00)
Wyndham Sugar Bay Resort 7.50(5.00) 9.00(6.00)
Yacht Haven Marina 2.50(2.50) 4.50(3.50)

Hello Vicki,

Take a taxi from dock to Secret Harbor (around $13 a person one way). Then take a taxi from Secret Harbor to Sapphire Beach (not sure perhaps $5 or $6 a person) and then return to the ship from Sapphire to the ship (around $12 a person). If you are 2 or more people you might want to rent a car for the day... Budget and Avis have offices walking distance from the dock.

Additionally...
Taxi prices are available on this site under Transportation, there is also a special cruise guide section that includes some of the frequently visted destinations of cruise passengers that you might enjoy; at the top of this site click on General Guide and then Cruise Guide.

Enjoy!!

--Islander

Ya'll have been so helpful , thank you for the advice. vjb