My husband and I really enjoyed our stay at Annie's Place. Communication with Andrea and Joanna was great, and Andrea organised a transfer from the airport for us which made check in very smooth.
Mdina is absolutely beautiful; it was amazing to be staying right in the middle of this special place, and we loved the old stone of the apartment. The apartment is lacking in natural light, as others have said, but if you're going to be spending most of your time out and about exploring Malta (which you should!), that's not really an issue. At the time of year we went (March) it was also a bit cold - there was only one electric heater, which wasn't really enough given the size of the apartment, and it's not allowed to have it on at night or when you're out, so it was particularly cold when we arrived back after a day out and in the mornings. So if you're going in winter I would advise taking warm clothes to wear inside (there are also spare blankets provided), and something to wear on your feet inside as the stone floor is also cold.
All in all though we would highly recommend Annie's Place. My coffe-lover husband also wanted me to mention that the coffee provided is top class!