When interacting with foreigners who are not able to speak Estonian, do the Estonians prefer Finnish to English? Does it depend on the area, e.g. is an Estonian more likely to be able to communicate in Finnish in e.g. Tallinn? For a Finnish tourist, would it be considered more polite to go with English in say a restaurant?
Your best bet is English, since to a first approximation, everybody you're likely to encounter in Estonia speaks English.
Fluency in Finnish is fairly low and declining, especially among the post-1990 generation who grew up watching English media, not Finnish TV. While the languages are closely related, the pronunciation and vocabulary is sufficiently different that the spoken forms are not mutually intelligible without considerable study, and it would be a little rude to just assume people speak Finnish. Still worth a try if English clearly isn't getting through, but ask if they speak Finnish in Estonian first ("Kas te raagite soome keelt?"), and Russian would likely be a better bet.
And yes, there is some regional variation: Russian-speaking Estonians, most of whom live in the east, are even less likely to understand Finnish.
Source: personal experience as a Finn who has often visited Estonia, speaking only English and the odd word of Estonian. I can't recall the last time I had to trot out my Finnish there.