Grand Cayman is the most friendly, safest of the islands I've visited. It is very easy to hop a city bus or a cab to one of the main beaches.
The two best tourist spots are probably the turtle farm and stingray city. If you do the turtle farm thru Boatswain's web site, it includes a discount on tickets and transportation to/from the location. Again, easy. We did it as part of an island tour (same price as turtle farm alone!) and they offered a drop off at one of the main beaches or at the tender port.
ALL beaches are free to the public. There are little brown road signs that indicate public access to the beach (while the beach is free, you can't trespass on private property to get to the sand). The main places (7 Mile and Sea Grape) will have vendors with chairs, toys, food, etc. We really haven't explored the port area much...there are the typical shops, a Dairy Queen, etc. The biggest thing is that the island is clean, relatively safe, etc. If DH wants to explore on your own, go for it.
Captain Marvin's "store" is right next to the DQ. This is where you check in for things booked thru them. I don't know if they can handle "walk ups" if you were to choose that without an excursion booked.
OK, my take on GC is that it really isn't a lot like Nassau. There is the obligatory building at the tender port which looks like a flea market, but after that, this is a NICE port.