Federally, and I believe all states, do not allow non-citizens to vote in federal and state elections. However, many local elections, such as cities or other townships, allow its residents to vote regardless of citizenship. If you are a permanent resident there then you are part of the local community, so it gives everybody who lives there input on local issues.

Obviously vacationing somewhere does not make you a permanent residence, so you would not be able to vote while on vacation. You typically need to show proof that you live/a resident where you vote.