I returned a few days ago from Gems of Baltic cruise on HAL. Arrived and departed from Copenhagen but had no opportunity to explore the town.
TALLINN; An absolute picture-book of a place. We walked to the Old Town directly from ship. No hassle exiting port -- in fact, the people at the gate were very helpful (we had to show only our cruise pass). Maps and brochures were readily available as you exit the port. It's about a 20 to 30-minute walk from ship to Old Town. Bear in mind that much of the Old Town is uphill on cobblestone streets. It was very hot and humid during our stay (unusual for those parts), which was draining.
We then decided to book excursions through the ship for Helsinki and Stockholm so as to get an overview and then stayed in those cities at the end of the tour.
Our ship had a continuous video giving excellent directions for each port, and maps were handed out as we exited the ship.
We saw the red two-decker hop-on busses just outside the port gates in Helsinki and Stockholm but were happy we opted for the tours, as time is limited on such a port-intensive itinerary.
Have a wonderful trip!