We have just returned from a week in the Annexe. We had a 1 bedroom apartment which, although very basic did offer everthing that we needed. My only grumble would be that the pillows were a little hard. The room was cleaned every other day by Vasillius who also owns the supermarket next to the appartments. The rooms overlook a courtyard and the only noise that woke us was the cockerel that wanted to announce morning. All rooms either a balcony or terrace.
We went by bus into Kos Town from Tingaki, it cost €1.30 each way and the bus station in Kos Town is right near the old town. There was the usual array of shops geared at the tourist, your chance to buy Rolex and other fakes. A wide range of places to eat all vying for your trade but we didn't feel preassurised by anyone to eat there. There is plenty to see and do and it can be done in a day (or 2 if your girlfriend has forgotten her Mum's present). It is gently sloping for those that are not too energetic on their feet and all sights can be reached by foot.