I have visited Tallinn twice and each time stayed in hotels that were wonderful--anything in the ring of the exquisitely charming Old Town walls will be especially desirable for ease of exploration, though there are several things worth seeing outside Old Town. I will also recommend looking into guided tours by EstAdventures--they do walking tours as well as small group day tours, I took 2 and got to see Haapsalu, Lahemaa falls, a monastery ruins and 2 manor houses and much more in outlying areas, I was there past the tourist season so one trip was just me and a couple, the other was me and the delightful owner of the company was my guide.
First trip I stayed at the Hotel Savoy, just at the edge inside Old Town. Second trip was May of 2019 and this time I chose the Von Stackelberg--and will stay there again-- which was the magnificent home of a baron and is just outside the walls, a 5 minute walk past Alexander Nevsky cathedral and a lovely park and you're in the old town. Also 5 minutes to the Museum of Occupation & Freedom, and in a different direction 5 minutes to the Balti Jaama Turg, a really interesting indoor marketplace of food, hand crafts and antiques vendors. Tallinn is known to have a great Christmas market which is in the town square, and for indoor activities I enjoyed visiting Kadriorg park and touring the palace and also the KUMU modern art museum--a short tram ride will get you there.