I have stayed at a few of the Villas around the area. There are several on the headland the opposite side to the White House and I would say that these are all walkable into Kalami. There are steps down the side of Anastasia where I have stayed in the past which lead down to the road, It is a pleasant walk down to the bay, though the steps back up wore me out after a few drinks! I would imagine that those staying at Kouloura or Kalami Bayview and the other villas begind Myra & Anastasia would/could use these the steps down to the road too, but I am pretty sure that there is a track too... failing that the road is not too long! My only personal concern is that most of these villas are operated by Thomsons.
I am pretty sure both Meon and CV have a couple of others in the immediate area that would probably be walkable too.
Slightly further away, overlooking the bay is Villa Emilios (Agni Travel)which we have only recently returned from... this Villa is stunning and the views are amazing, the web site although showing spectacular pictures just does not do the villa justice. The drive into Kalami is no more than 10 mins. I believe that there is a track down the side of Villa Nikos but it is about 45 minutes, and probably longer coming back up. There are other villas in that general direction (Vigla/Vingla) such as Rastoni whic also offer wonderful views, or at least did when I stayed there a few years ago. I would say that a car is essential for these villas
Whenever we wanted to go to Agni we took the car down to Kalami and got the water taxis around to the bay, it it a much easier way than driving round, and more pleasant too!