If you want to buy new furniture, there are few options immediately 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 three IKEA stores about an hour away in Philadelphia, PA, Conshohocken, PA, and Elizabeth, NJ. (New Jersey has lower sales tax than Pennsylvania.) IKEA should also deliver, although there have lately been supply chain issues with many retailers. There are a few options for furniture and houseware nearby in Marketfair and other strip malls on Route 1 (e.g. Homegoods, Home Sense, Target). Buying from Amazon, Wayfair, and other online retailers is another popular option.
Many graduate students choose to purchase these things used. 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 items are the GSG slack, Facebook marketplace, Craigslist, and Princeton’s TigerTrade. Sellers on Buy Nothing groups on Facebook often give away things for free (there are a couple groups for the Princeton area).