Suomenlinna has to be top of your list, especially if it isnt raining.
I would also recommend walking out past the Silja ferry terminal along the shore to Cafe Ursula (Coffee and snacks) and beyond.
I would expect Helsinki to be closed on Friday, Sunday and maybe even Monday. Saturday will be like a normalish Saturday. Finns dont yet relate bank holidays to shopping.
Helsinki is not the most exciting place to visit, but neither is it a waste of time. Plenty to see and do for a few days.
And, yes, watch the seagulls, especially in the market square.