Ok first, the decor downtown will be in the Renaissance area, Rif Fort (right off the ship), Otrobanda on the Brionplein and the Queen Emma bridge has lights and in Punda normally in the Wilhelmina Wilhelmina Plein, all within walking distance of the port (5 to 10 minutes depending on how fast you walk). The Christmas tree is normally on the Punda side right after you walk over the Queen Emma bridge.
A few stores in Punda usually are open on a holiday when a ship is in port, again historically from maybe 10 AM to 2 pm.
West side beaches are about an hour from port and unless you take a tour, renting a car is your best option.
Mambo beach area is close to port but not like the West beaches with cliffs, etc. but there are shops there (honestly not sure if those will be open on Christmas day).
Please keep in mind that our beaches will be crowded with not only cruise ship guests, but other tourists and locals as well.