Nothing is really far from Duval St but when you dock at the Naval Station you must use the Conch Train
to leave and return to the base. This is a low-level security measure. You can't walk to town. However, this is also good because the Conch Train drops you off down at Mallory Square which is near everything. The train is complimentary for the passengers to ride to and from the ship.
Calica is a commercial pier used for convenience. There are no "free" beaches there. You have to go to Playa del Carmen for that - just a 10 minute or so taxi ride away.