The highest hill on Kaivopuisto is a good spot.
Best to take photo towards the sea to avoid Helsinki's light pollution so use an app to predict when your target patch of the sky will be pointing toward the southern sea.
There is an observation tower there (https://goo.gl/maps/zuKt2dhhB8oydGPU8)
Check with a light pollution map. You don't have to avoid the city too much to get a good pic of the night sky. But if you're close to a city, be aware that longer exposed pictures will get a yellow-ish tint from all the high-power street lights. From my experience, anything under 10 secs (f/2.8, 16mm, ISO 640) is fine. But with shorter exposure time, you don't see the color details of the stars.
Light pollution map
Some other locations that I have yet to try:
Wait until it's dark (duh?). But actually in certain regions of the world, for some period you don't have true night. Check from a night sky rhythm chart.
Sunrise and sunset times in Helsinki
It's a bit challenging to go stargazing in Finland because when the weather is nice enough to get outside at night, you don't have true night anymore...
Also check the cloud map beforehand. I use this one for Finland:
Anticipate certain interesting astronomical events like lunar eclipse, meteor shower, etc.
Calendar of Astronomical Events 2020 - In-The-Sky.org
Starting Astrophotography? Here's What I'd Do:
Use your lens hood to avoid unwanted light pollution
Focusing at Night: A Tutorial