There's a ye olde restaurant in the central square of Tallinn, which is pretty funny. It's decked out like a medieval place and they offer you 'your weapons' when bringing the cutlery, etc

. It tickled me, at least.
Presumably you know about Suomenlinna, but I'd probably take a trip out to that for sure. I can't remember when all the stalls at the central harbour/dock/whatever stop selling stuff, but if they're still there you can get a load of nice fish for a decent price (massive hunk of salmon, a load of whitebait, etc, and it's pretty tasty). Then near there you'll find the old market which has a load of stalls where you could grab a nice reindeer kebab

.
It depends how much time you have, really - there are the two cathedrals near the central square, then I'd have a wonder around that area and the harbour (the central square and harbour where the food stalls/old market/ferries to Suomenlinna leave from/etc are really close to one another. If the harbour market isn't there, you still have the option of the restaurants on lightships/in that area. I'd love to be able to say I'd eaten in all the restaurants, but when I lived there I was a student and made use of the Unicafes (student price meals for 2.50€

). If you stroll in the direction of the railway station you'll also get to the museum of contemporary art/their parliament/etc.