If money is an issue, look outside of Hanover/Norwich. White River Junction, VT has a few (relatively) clean and update chain hotels that could work and they're only 5 minutes or so from campus. The problem then becomes how do you get from your hotel to campus. Public transit is limited up there, so you could be faced with a dilemma of (a) pay more money and stay very close to campus (i.e. the overpriced Hanover Inn or the further out, but fairly new Mariott (which has a shuttle) or (b) stay further away, but rent a car to get around.
I suggest you check out priceline.com for hotels in the area. Before booking a place, call them to see if they offer complimentary shuttle service to Dartmouth. The Dartmouth Coach provides comfortable bus service to and from Logan Airport in Boston, so it is possible to get to Hanover without a car.
I'd suggest staying somewhere comfortable/clean/new the night before your interview so you aren't traveling the whole day before interviewing. If you have reward points from a credit card, you might be able to get a free night in your hotel or a free rental car.
You can read more about how people have traveled to Tuck if you read earlier posts in this thread.
Good luck and have fun.