Mimi, we were in Montego Bay in 2001 (Carnival Inspiration). Took a cab over to Doctor's Cove Beach. Very reasonable fee (maybe $3 pp); chair & umbrella rental available. Access to cold drinks & snacks. Very clean, very friendly beach. Fresh water showers (indoor & outdoor) and restroom facilities.
Left the beach and headed to Margaritaville for the best frozen fruit concoctions! 110 ft. water slide was awesome, as well as the water trampolines. Cabbies literally swarm as you exit the restaurant's door, waiting to take you back to your ship.
As previous posters mentioned, the area is very poor. Hustlers everywhere trying to sell you anything and everything! Good t-shirt shops along the walk from beach to Margaritaville; good deals, but be sure to comparison shop.
Have a great time!