We did our shopping in the stores that were just walking distance from the dock. Merchants were very nice there as well as the straw market. There we walked to Junkanoo Beach and spent the rest of the afternoon there.
We took a taxi to Port Lucaya marketplace and did our shopping in the straw market ($10 round trip; taxis are easily available once you step off the ship). The straw market workers were very friendly and more than willing to work out a deal. Much to our surprise, however, we learned that there were better deals on the cruiseship; you could get shotglasses for 88 cents on the boat, compared to $2.50 in the straw markets. However, no straw market worker was willing to sell a shot glass for less than $1.