"Your voter registration is tied to where you live. As a college student, you can usually register to vote in either your hometown or where you attend college, depending on the residency requirements of your state. Keep in mind: You can live in more than one place, but you are only allowed to vote in one" (https://vote.gov/guide-to-voting/college-student).
Choosing between your college town or your hometown
If you are going to college outside of your hometown, you may want to consider the following:
Who is on the ballot in each place?
Are there local policies/issues that are important to you in either place?
Which location is more convenient for you?
Note: "Where you register to vote will not affect your federal financial aid, including FAFSA, Pell Grants, Perkins, or Stafford loans. It may affect whether you qualify for in-state tuition" (https://vote.gov/guide-to-voting/college-student).
Voting in your hometown
Register to vote using your permanent address in your hometown.
Use your college address as your mailing address on your registration.
In New Jersey you can request a mail ballot if you're unable to vote in person (see Mercer County Vote by Mail Page). You can have the mail ballot sent to your college address. After you complete your Vote-By-Mail Ballot, return your ballot by one of three ways, mail it back, place it in one of your county's Secure Ballot Drop Box Locations or return it to your County Board of Elections Office.
Voting in a different town in your home state
If you moved to a different county in New Jersey to attend college and are registering with your college address, you must have resided at your new address for at least 30 days before the election to be eligible to vote from that address (https://www.aclu-nj.org/en/news/how-vote-new-jersey-elections-college-student).
After confirming your eligibility, you can register to vote using the street address of the building where you reside, either on or off campus. While you should not use a campus mailbox address to register, you may use a campus mailbox as your mailing address. If you are unsure which address to use, contact your school's civic engagement office or the local election office.
Use a polling place locator to find out where to vote
New Jersey allows you to ask for an absentee or mail ballot if you are unable to vote in person (or would simply prefer to vote by mail).
Voting in your college town out of state
In some states, you must live in the state for a certain amount of time before you can register to vote there. Check the residency requirements for voting in your college state on the election office website.
After you confirm your eligability, register to vote in your college state. You can register to vote using the street adress of the building where you live (either on or off campus).
Don't use a campus mailbox as your mailing adress. If you are not sure what adress to use, contact the civic engagement office at your school or the local election.
Most counties and states don't require you to cancel your voter registration after you move, but doing so can help your local election officals. Many local and state election offices have forms you can submit to cancel your registration. To get voter cancellation forms, find your state or local election office.
Voting during study abroad
You can vote from anywhere in the world if you are a U.S. citizen!
You will need to fill out an absentee ballot using the Federal Post Card Application (FPCA)
Your voting residence will continue to be your last residence prior to leaving the U.S. for study abroad.