I just went to Tallinn for a three day weekend.
Museums: Tallinn City Museum and the Estonian Occupation Museum were our favorites. We also liked walking along the city walls and underground in the battalions.
Bars: Whisper Sister (you need a reservation)
Restaurants: Farm, Rado and Rastaskaevu 16.
Breakfast: Pub Kompressor and Van Kook.
Coffee: Varav and Fika Cafe.