Awesome that you're in Tallinn; it's a gorgeous city and I've been there plenty (even worked there last summer).
If you're still there, go eat at "Kehrweider's" coffee shop - it's my uncle's and is right in the main square (Raekoja plats) beside the oldest pharmacy in Europe (or something like that), the Raeapteek. Everyone likes the coffee there, and the Estonian beer.
Naturally, I've hunted all over the city for coins and there are about 20 antique shops with coins, and of them, about five are run by reasonable, honest people. In all of them, initial prices are very high as they are tourist traps, but I've always been able to bargain quite aggressively (though perhaps seeing as I'm Estonian they are more generous with me). What a lot of them say is along the lines of "sorry, I don't run the store and can't go any lower on the prices" but really it's BS and they will bargain.
Assuming you're still there, go to "Idla Antiik" on Olevimägi, close to Pikk street (it's across the street from Hell Hunt restaurant). My family in Estonia is close with the Idla family, and from what I saw, their coin prices are quite honest. The guy in charge of coins is a kid in his twenties named Georg (I can give you his email if you'd like; he speaks fluent English).
Another pretty honest place is "Aigis Antiik" on Kinga street. A place called "Shifara gallery" has very nice coins and knowledgeable dealers but the prices are often high. You'll find that generally the Baltic and Russian stuff is more expensive in Estonia than it might be elsewhere, say in Canada or the US.
Please message me if you want more information and have/I hope you had a lot of fun in my favourite city in the world!
Numista referee for Canada and Estonia.