I think a good place is Viru Square (Viru väljak) it's practically attached to the historical center and there are several spots, like the Sokos Hotel Viru or the Viru Keskus shopping mall.

From airport there is the line number 2, bus stop A.Laikmaa

I think a good place is Viru Square (Viru väljak) it's practically attached to the Historic Centre and there are several spots, like the Sokos Hotel Viru or the Viru Keskus shopping mall.

From airport there is the line number 2, bus stop A.Laikmaa, the ticket price is 1.60 €, according to this page