We basically looked at what the market pricing was, and adjusted for lack of agents fees. (we split the saving of the agents fees).
Actually, we also bought our PPOR after knocking on the door.... and we used the same approach to work out the price.
I guess in both cases there was a strong desire to sell. We were on a main road, and selling to the neighbour was our best chance of getting a good price. and the previous owner of our PPOR had the house on the market for over 6 months...... so it probably depends whether your neighbours have any motivation to sell.