Just returned after spending two weeks in Anastasia Apartments. (Room 8 upstairs) Plenty of space -double bed in bedroom plus two good sized sofa/single beds in the living area. We had two balconies (one each end) both with good views of the bay. Well equipped for cooking (if you want to be bothered!) - a small combination oven/grill with two good sized cooking rings on top and a full sized kettle!
Decent sized bathroom with a shower curtain!
Supermarkets stock the essentials but are very limited if you want good fresh meat and veg. I would suggest a trip up to the top village or hire a car and go to one of the large supermarkets at Tigaki, Kardamena or there is a very good "Champion" on the main road into Kos town.
The resort is very good but definitely could do with a local taxi service or even a "Happy Train" as it can be a bit of a strain on the old legs walking around the bay or up to the old village.
An apartment to be recommended - but you need to book early as it is very popular.
Happy holidays!!

The apartments are between Faros taverna (which is virtually on the beach by the harbour) and a small supermarket. There are two large trees by the entrance gate to the apartment block.