Arthur Avenue: I go there to market-- fresh pasta, wonderful mozzarella, great butcher, etc.
Both restaurants on Arthur Avenue (mentioned up thread) are good. However, prefer the restaurant at the NY Botanical Garden, Hudson Garden Grill, more sophisticated, but not stuffy, chef & wonderful vegetables. It opened this past spring. (The menu is online at nybg.org)
The suggestion about campus newspapers is excellent. Some of them are online, so you can read back issues.
Even if Tisch at NYU is not what your daughter is interested in, the East and West Village is an area that college students gravitate to. The residential areas in the West Village are lovely to walk around. And, if you have the time, you can walk on the High Line or take in the New Whitney Museum. Great restaurants in the area, too!
Thinking of food reminds me that one of my fondest memories of college touring is finding interesting restaurants of all sorts to enjoy with our then rising senior.
Accommodations: Years ago (maybe still) one could get reasonably priced rooms at a Comfort Inn on the Upper West Side, it’s a block away from Central Park in the West 70s. The suggestion of staying near Sarah Lawrence is convenient for driving to Fordham (in the Bronx) or taking MetroNorth into the City. If you were to stay in Ft Lee, you could take a bus from the NJ side of the bridge (GWB), then catch the A-train on the Manhattan side of the GWB. You could also drive across the bridge and easily park your car near the Cloisters and catch the A-train. Another thought, if you’re in Manhattan on 4th of July, is to book a room on the EAST side with a view of the fire works.
Have fun!