When using the phrase "two towns over", how many towns are in between the locations in question?

Solution 1:

Merriam-Webster gives the relevant sense:

over [postposition] on the other side of {an intervening space, location etc}

  • the next town over

(POS adjusted [compare beyond the next town, where 'beyond' is obviously a preposition] and otherwise slightly adjusted)

So 'two towns over', though it sounds rather unidiomatic, would be 'beyond the next town but one'.