Hi Surreymaid and welcome to the Forum.
It may be that you will have to have more than 1 Apartment!
Bearing in mind your requirements - you will not want anything up the hills!
I would suggest the Barras Apts. (Thompsons),
Thomas Bay Hotel (Thompsons)
Theodosia Apartments (via San Stefanos Travel -
http://www.san-stefano.gr/ )
- they have some nice v/large Ground floor Apts for 4+ people, with adjoining Apt for 2 if you want privacy, discuss it with Noula,
Leonidas Villas (own website -
http://www.leonidasvillas.co.uk/page_1225111430531.html ) - Noula will do the transfers for these as well!
All these are on the flat, near the beach, are disabled friendly with good and easy access and should be the best for you.
All have Apartments / Rooms that have ground floor / ramp access, all very good.
These should get you a good start!!