I took a taxi to Chankanaab Park. I've been there before and swam with the dolphins and a seal. Today I swam with a couple of manatees and fed them lettuce. It was great because there were only three of us and two manatees. When you swim with the dolphins there are ten people and only one dolphin. Chananaab Park is a great place to hang out. Taxi service between the port and the park is easy to get and very inexpensive, especially if there are two or more of you in the taxi.
Grand Cayman has a high standard of living, so you will not be bothered by street vendors. I planned to take a taxi from the port to the Turtle Farm, but did not realize how far away from the port the Turtle Farm was. It is $30+ each way, so I didn't go. However, many people offer independent tours from the dock for $15 and the one I took included a stop at the Turtle Farm for 30 minutes for only $10 more. Stingray City is also a favorite here, but the town of Hell is not worth going unless it is a side visit while doing something else - and then only once.
The little village next to the dock is interesting. I didn't check it out 100%, but I did enjoy it there after returning from my shore excursion to the Swamp Safari Village. That is where the famous scene of James Bond running on the backs of the crocodiles in Live or Let Die was filmed.