Tallinn and Helsinki

Tallin, just walk around the old town. It's not that large. Do be aware that since you are on a cruise ship, there will be hoards of tourists.
Helsinki - take the #3 tram -get on at the outside market. It goes in a figure 8 route. Takes about an hour. The harbor behind the Russian church is a pleasant walk.

These cities are covered in Rick's Northern European Cruise Ports book, along with Amsterdam and perhaps some other destinations of your cruise, or in his newer Scandinavia guidebook. For just a listing of top sites without the details, see http://www.ricksteves.com/europe/finland/helsinki.

An open-air folk museum gathers historic culture and rural architecture that you don't really get in a big city. Both cities have them, as do other regions. To get to Seurasaari in Helsikini (only open mid-May to mid-September) you could take bus #24 from top of the Esplanade (20 minutes each way).

In Tallinn, the old town is amazing. See the Russian Cathedral and old walls. If you have time, take the tram out to the Peter the Great cabin and Catherine the Great's palace (Estonia was conquered by Russia during Peter's time).

In Helsinki, wander the harbor market area, Cathedral, Russian Cathedral, the main park that runs out from the harbor and the train station (designed by Eliel Saarinen).

Both cities are small and very walkable. But they also have great tram systems to get to further reaches or to save time.

My wife and I are planning a visit that will also include Tallinn and Helsinki in June 2016. What is the distance (feet or meters) between the Cruise Ship Terminals in both cities to the nearest tram/metro stop? Where can a ticket/day pass for local public transit be purchased? Are the tickets/passes purchased at automated kiosks or are they purchased from persons? We have had little success in using our US-issued "chip and PIN" credit card at automated kiosks and we suspect it won't work in Estonia or Finland.

Is there a tourist information office near the Cruise Ship Terminals? The ships are pretty stingy when it comes to providing maps unless you are signed up for a ship-sponsored shore excursion.

Jon--You might want to start a new thread for your question, Estonia unfortunately doesn't get a lot of traffic on this site. I visited a couple of years ago--Tallinn for a week and day trip to Helsinki--and absolutely loved it. I wasn't on a cruise ship so can't answer your questions, but will just say I found it easy to navigate their trams and buses, taxis also not a problem to get into the main areas you'd want to explore in either town. Each can be given a good exploration with just one day, but there's also plenty more if you have the time.

Christa:
Thanks, I follow your suggestion.

Jon: It's about 1/2 mile from the cruise docks to the main square in Tallinn. We found a great brewery close by. It's another 1/4 mile hike to the top of the hill and the old city. Mass transit's not required in this city.
The Hop on Hop off buses are sitting beside the cruise port in Helsinki. It's the best way to see the town.
Don't worry about using credit and ATM cards in Scandinavia. People there virtually use no cash--and charge the smallest of purchases. Pin and chips are accepted everywhere, as is the old style U.S. credit cards where you have to sign for them.
We just loved every city the cruise ship stopped at, including Tallinn and Helsinki. We also went over to Oslo and took the Norway in a Nutshell trip through the fjords to Bergen, Norway.

The stops in Tallinn are often short, the time in port depends on the tides. I was among the first in line to disembark when we docked on schedule at 7 am, walked to the Old Town and had a good deal of time to enjoy the town as it was waking up. It's a small area so a couple thousand cruisers - plus the many overnight tourists - fill the town up. There were lots of handicrafts (mainly wool knits) in the market and at least one shop to watch the artisan blowing glass. The town is so picturesque, I couldn't stop taking photos.