We just visited Tortola on the Rotterdam at the beginning of June of this year.
It as a beautiful island to visit. We took the Tortola Highlights tour which entailed a tour of the island in an open safari type of truck from the end of the pier area. We were very lucky to have had a GREAT DAY weather wise. It's $29pp and had one tour leaving in the morning and one in the afternoon.
The tour entailed a complete ride throught most of the island. Many of the stops were at lookouts that were breath-taking from atop the island. WHAT a ride up the mountainside to get to these points, WOW. We got to see the neighboring islands especially St John's which I have cruised over 13 times in the past including to St John's and never knew that it was that close by.
The one lookout at mountaintop was also near a observatory. There we had a 15-20 min stop and got a complimentary. We proceeded again thru the island to Cane Garden Bay Beach. There we were given a complimentary drink and about a 1/2 hour to use the beach. It's all they descript. Crystal Clear waters and beautiful sandy somewhat private beach.
After we proceed back from the beach to the ship. When we got close to the town/ship, an offer to leave the safari truck to roam the town was announced. Some people did do so and were dropped off.
It was announced during the onboard island discussions held that it is about a 15-20 minute walk to the town from the ship or back to the ship. Taxi's are available at the end of the pier pass the security zone for hire. Also, it was mentioned that if you go on your own you are responsibile to return in time before the ship leaves. I know that was especially stressed about self touring of Virgin Gorda which involves a use of a 15-20min ride on a ferry across the harbor.
We were not aware of anyone with us did their own tour thru a taxi.
Good Luck on your tour planning.