I don't know about the shops in Miami, but if you are going to buy duty-free you might as well do it on the ship. The ship will not let you take your duty-free purchase from land to your room--they will hold it until your last night on the ship, the same as when you make a purchase of duty-free onboard.
You can find liquor stores in Little Havana off Flagler street. The area is just West of Bayside. Duty free is only available if you are flying in from outside the country. Otherwise, as Zoomer said, you can buy on the ship providing you are not counting on it to use while at sea.
Spirit Jan 18th,
Sovereign of the Seas12-97