Upvote:2
Within Viru Square, I would arrange to meet at the (Viru) Gate, which is the entrance to the Old Town.
Upvote:5
I think a good place is Viru Square (Viru vรคljak) 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 โฌ, according to this page