I stayed in Tallinn for three months as my studio was part of an Accelerator program there. The people are absolutely great even though they may seem a bit cold at first. They really like to drink! I stayed the the FeelGood Hostel on Tonismagi right on Freedom Square. It is cheap, clean and has warm and friendly hosts. Travelling inside Tallinn is super easy with the bus cards, which allow you to use any bus or trolley. Other than that the Old town of Tallinn which is the medieval and most beautiful part can be completely explored by foot. There are beaches nearby Tallinn as well and summers are really nice. I had the change to stay a bit in Winter, Spring and then a few weeks of Summer so I got to see the change in the people with the change in the seasons. In the winters Tallinn gets as cold as -30 and below. It is virtually pitch dark for most of the day in winter, but expect sunlight till 11pm in the summers. If you are lucky, in the winters there are rare sightings of the Aurora Borealis, but Finland is a much safer bet for that. Tallinn is quite safe although there are hardly any Indians around (Expect STARES!)
Some of my favourite places did not have Google locations so I am going to list them out here.
Müst Puudel: The most chilled out and cool restobar in Tallinn. Food is great and so is the service
F-Hoone: Awesome Restaurant and Coffee shop by day and a club by night. I totally recommend a lunch here
Shooters and Nimeta: A highly touristy shot bar (Shooters) and an after hours late night drinks place (Nimeta)
The Black Hole: A freaky late night bar in the cellar of an old building with no ventilation. It is, atleast, a once in a Tallinn visit experience.
Maritime Museum is a must go. It even has even has a submarine!!!!
KUMU is a huge museum for arts. They had some amazing exhibits when I was around. They have a nice cafe. The museum is facing Tallinn's largest park, Kadriorg, which is full of picnic-ers in summer.
Please try A. Le. Coq (my favourite) and Saku, both local beers.
Really awesome Medieval themed restaurant set in the picturesque Old Town of Tallinn. They have taken it so far that there is no electricity. However, there is free WiFi! As in Estonia there is free WiFi even in the forests!!!
Only downside is that this restaurant is very expensive.