Yes, Helsinki can be a depressing city during winter, but how Sami Yaffa and the crew gives you a quite bad picture of the city. And yeah, you should spend 42 minutes for watching the episode and visit Helsinki. During winter and summer to get some perspective.
Here is my places to be visited for short break in the city.
Day 1:
For lunch go to Konstan Möljä. They serve traditional Finnish cuisine with great price/quality ratio.
You need to check out the Hakaniemen kauppahalli's marketplace. Funny, that Tony did not visit the place. It has a great variety of meat, fish, vegetables, pastries, etc. That is a must for any food enthusiastic.
Sauna is a Finnish tradition. Go to Uunisaari, you also get a view towards the city and during wintertime there is possibility to take a dip through a hole in the ice. Freezing thing to be done, but you have try it out once.
Ateljé Bar at Torni Hotel has the best view of the capital area. Drinks at American Bar downstairs are better, but go all the way to the top for the drinks. The view from ladies room is not bad either.
Dinner at Muru is a must! Just make sure, you book in advance. Should you not manage to get a table from there, visit Ravintola Aito.
After dinner drinks at A21 Coctail Longe and then of to Bar Loose next door for some rock. They serve good hamburgers as well. Excellent to avoid the hangover.
Day 2:
Breakfast at TinTin Tango. They serve breakfast all day long and should you also need to use laundry services, it is available on site.
In summer the next stop is Linnamäki amusement park. The 60+ years old wooden roller coaster is a must! It is Classic! Yes, with capital C. Linnanmäki has some restaurants, but you are way much better of going to close by places like Soul Kitchen, Bullman or Cella.
Feeling too hang overish? Go to Hietaranta for tanning and chliing and babewatching.
Should you visit Helsinki in winter time, make sure that HIFK is playing at Jäähalli. Viisi Penniä bar/restaurant is also located close by.
Want to have dinner with a view? Then travel to Espoo and eat at Haikaranpesä. It is on top of a water reservoir. Don't wan't to travel to Espoo? There are always Lehtovaara, Savoy, Gaigin, Manala, Sasso, Töölönranta...
From and to the airpoort take a taxi. From Tallinn and Stockholm you can always take a ferry to downtown Helsinki.