I definitely recommend you to take a day trip with ferry to Tallinn if you don't need visa.
Likewise, if you don't need visa, a cruise to Stockholm, Sweden is very recommendable, they depart around 5pm from Helsinki, you spend overnight onboard, a day in Stockholm, overnight onboard back to Helsinki. And the cruises are dirt cheap.

For car travel, I definitely not recommend to drive to Kotka, you will be bored by the highway which offers little to see (no scenic route) and the city is dull. I recommend to stay instead in Porvoo, which is closer to Helsinki and much more attractive city.

Alternatively, you can drive westwards to Turku, the anterior capital of Finland which is historical and very nice, at less 2 hours drive from Helsinki. Actually Turku is the first choice I recommend for people who want to explore something else than Helsinki.

Sadly, in March, the Finnish nature cannot show the nice side of it. It will be pretty grey and dull if it is raining.