The port itself doesn't have too much to offer. We took a van/taxi to Lucayan Beach for $5 per person-one way. (price is posted so you know what each trip will cost) Once the taxi dropped us we found a small area with very limited shopping but several restaurants. We had just had breakfast on the ship so we weren't looking for food. We walked to the beach but was disappointed to find a very small beach area with no shade. We had to carry our own towels from the ship and there were only 2 porta pottys available at the beach. No place to change, etc. There was a bar and grill area but seating was very limited. The place was packed with people from the 3 ships that were in port that day. My family did rent wave-runners ($70 for 30 minutes) This was lots of fun but pretty costly for only 30 minutes. I would not go back to this location again. I've read there are other beaches which are not a busy...I would encourage you to check them out. The taxi rides felt overall safe.
We had a better experience in Nassau. When we got off the ship we saw a free shuttle which drove us from the ship to the shopping (located at the port)
There is both inside and outside shopping which was crowded but fun. There is plenty to do if you just want to wander from shops, restaurants, etc. We read on the web about the Sheraton day pass. We walked outside the port area and saw a port ambassador (nice lady) who told us where we could get on bus 10. We walked about 4 blocks and found bus 10. We paid only $1.25 per person and the bus driver dropped us off in front of the Sheraton. We went in the lobby and asked or purchase a day pass. It was $75 (2 adults, 2 kids). The day pass included use of the pools, chairs, towels, ocean, beach, and non-motorized toys. Since the ocean was rough that day we didn't get to use the toys but saw they were available. It is a beautiful place with a great view, shade, tons of chairs. For the price of about 1 or 2 excursions we got to enjoy all this space, clean bathrooms, and a restaurant/bar if we wanted. When we were ready to go back to the ship we walked outside the Sheraton and found the bus sitting at the driveway. They run about every 10-15 minutes. The bus was used by several locals getting to and from work, etc. Overall we felt safe. This was a relaxing day with lots of space to our-self. (Fall of the year so there were few hotel guests to share the facilities with.)