Hi Anna Jane
Debs & I have stayed in both Agni and Kalami. It is a hard choice but our personal preference is Kalami because you can more easily manage without a car. You have the tavernas there and the boat taxis to take you around to Agni as well. If staying in Agni you do have the tavernas there and can easily walk into Kalami during the day, but without driving you are limited to Agni Bay in the evening as I would not venture on the path at night.
Having said that we loved our stay in Agni, although we had the car we did not use it in the evenings and were happy with the choice of tavernas there of an evening and that was a 2 week stay.
I believe a lot of supermarkets will deliver now so you could probably manage in Agni without a car but I would suggest that it is advisable.
We have been having two trips there a year and tend to spend a week in Kalami with no car as it is that much more relaxing not having to drive, and then a 2 week holiday in the Agni/Kalami area with a car.
I know there have abeen a lot of threads on the accomodation and stays in the area, all very positive.
Certainly you will be staying in the best area of Corfu which ever you choose in my opinion!