If you want to buy new furniture, there are few options in Princeton other than Skillman's on Alexander Road, which tends to be outside of the typical graduate student budget. If you have access to a car, there are two IKEA stores about an hour away in Philadelphia, PA and in Elizabeth, NJ. (New Jersey has lower sales tax than Pennsylvania.)
Many graduate students choose to purchase used furniture. Unfortunately most students sell their furniture at the beginning of the summer, so students arriving in August or September won't always have the best selection. The best options for finding used furniture are Craigslist and Princeton's TigerTrade.