Church of the Rock and Suomolina Island.

Church of the Rock is unique architecture (but doesn't take long to visit).

The island, also called Svedborg (Swedish Fortress) is a UNESCO world heritage site. For a long time, supplying the fort was the reason Helsinki existed. You can walk walls and tunnels and see cannons/artilery dating from 1700's to WWI.

With time left over you can walk the city center/market area.

You can buy a transportation pass that includes busses, trams and ferries. We picked ours up at the Tourist Information office not far from the market square.

There is at least one tram route that makes some sort of circuit with many of the "attractions" either within view or close at hand so no need, necessarily, for an organized tour IMO depending on how fast you like to move.

Do you have a plan B in case the weather is poor?

The Jan Sibelius monument (see pix) is excetionally unique. You can hop a trolley downtown for a short ride to the beautiful park. The aformentioned Rock Church is easily accessible from downtown Helsinki, and Market days are held at the south harbor. Lunch at the venerable Cappelli's at the harbor. Famous Stockmann's department store is a short visit. You can fill the ten hours very comfortably. Oh yes..wanna try a reindeer burger..at the downtown MacDonald's. If you're "zoo" people, there's a very nice one out on one of the harbor islands. I didn't write the name in my journal.

Here are some scanned pix of certain sites in Helsinki and around the country. Just click on the magnifying glass icon to enlarge those that are three-to-a-page. Move the mouse around and they will be very clear.

http://picasaweb.google.com/stuarttower/Finland#

stu tower

You can easily take a bus from the airport to the main train station. From there you can walk/ride tram around the city center, walk the park, visit the waterfront, and visit the Russian Orthodox Church and the Lutheran Cathedral. Also a few museums in the area, but I'm not much for museums after an overnight flight.

If you aren't fading by then, you can take a boat out into the harbor or to the island or else a bus or tram up to the Church of the Rock. However, I would focus on just the area from the train station to the harbor for ease of navigation with jet lag and so that you aren't too far from the airport bus stop when you decide you are exhausted and need to return to the airport.

As mentioned, time of year and weather will affect your plans, but you can still ride the tram, go to the department store, etc. if the weather is too bad for walking.