There are plenty of hotels/apartments/hostels in the Old Town (Vanalinn) and City Centre (Kesklinn). Other popular locations, with many restaurants and bars, are Telliskivi and Kalamaja.
Here is a non-exhaustive list of options:
- Meriton Old Town Garden Hotel (in the Old Town)
- Kalev SPA (almost in the Old Town)
- L'Ermitage (just outside the Old Town)
- Park Inn by Radisson Meriton Conference & Spa Hotel Tallinn (just outside the Old Town)
Many more options on booking.com, especially apartments.