I wouldn't recommend being in the middle of Lyme Regis as it is expensive and parking is difficult. How about some of the villages nearby? Devon is cheaper than Dorset. Do you want to be in a place on it's own or with other cottages in the same complex? How far away do you want to be from the sea/pubs/shops?
Oh I'd given up expecting replies! Looking for the general area around Lyme but not right in it IYSWIM. Reasonable distance to beach - don't mind a bit of a drive. Never visited the area before so no fixed ideas really.
We stayed in charmouth, which was really lovely. Great butchers, crafty/second hand bookshop/coffee place, nice quiet beach with a fossil centre where they'll identify your finds for you-you can pick up ammonites on the sea shore in charmouth, you can't in Lyme. There's a good bus service into Lyme too. We stayed in a static caravan though so can't help with cottages.