We went to Tallinn in March and for a blow out evening meal i.e. three courses, beer, coffee and vodka each plus a tip the most we spent was �60.00 for the two of us. That was at Troika - a Russian restaurant. Other than that our average spend for an evening meal was between �15.00 and �20.00 each for more food and excellent food - than you could shake a stick at! Plus drinks.
As for things to do the views from Toompea across the city to the sea are wonderful, and Alexader Nevsky Cathedral with its recognisable 'onion' domes is well wirth a visit. Take a walk up Kiek in de Kok for more views, take a tram to Kadriorg where the Palace contains Estonia's Foreign Art Collection and - further in the park - the excellent KUMU contains Estonia's National Collection. The Tallin City Museum also gives a very good overview of the city and its history.
Other than that walk around enjoying the architecture and relaxed atmosphere. Oh and drink some vanilla vodka. It;s great.
As Kovac said the Ice bar is great, its located in the Merchants House Hotel on Dunkri. Also The Beer House opposite is quite fun, though the oom-pah music can get a bit wearing after a while!
Enjoy yoourself, Tallinn is a lovely city.