Depends on your income. If you want a nice, renovated flat in an attractive area, you're looking at 500-600+ euros a month, including utilities. Might be a bit less if you're in luck or willing to share a flat. As a local, I don't find renting in Tallinn very affordable.
Furthermore, not many areas with little shops, the Estonian speciality is mahoosive shopping centres scattered about the city. You'll find one in almost every bigger district. For independent cafes and lovely neighbourhoods, you'd be looking at Uus Maailm, Kalamaja, and Kadriorg mostly.