Well, it depends on what you want to eat. Then there's Teresa Caffe, which is really good, and moderately priced. I just found out that The Original Soup Man (you know, "No soup for you!" from "Seinfeld.") has opened a franchise in Princeton. That could be tasty and inexpensive. And it's very conveniently located in Palmer Square, which is a short walk from the Library. I like to go to Winberie's for pub type food.
Later on there are two places, even three, that have really good ice cream.
First, there's the Halo Pub. It's owned by a local micro-dairy, and is a local favorite. Then there's Thomas Sweet, which is legendary. The original one is near the Rutgers campus. They make their own chocolate and their own ice cream and they are top notch. I've loved them since my days at Rutgers, but I also want to mention that last spring they were generous enough to donate about 20 gallons of ice cream to our Homeschool Choir's end of year picnic. :D The Bent Spoon has organic ice cream, some of which is flavored with locally grown fruit. Unfortunately they close at 6 on Mondays.
There's also a Starbucks nearby on Nassau Street.
If you're staying at the Nassau Inn, all of these places are a pleasant walk away. A few of them are actually in Palmer Square, where the hotel is located.