Some useful web sites: Petrópolis - RJ , Petrópolis on line .
Places to eat: at LNCC there is a quite decente cafeteria, with
from 12:00 to 2:00 pm, and snacks the whole day, up to 7:00 pm.
There are some few other places around (walk distance) that are OK, The Alemão (up to 8:00 pm), and Pavelka (up to 8:30 pm). There is also the churrascaria Lago Sul. Otherwise, driving 10 minutes, you reach downtown and there is a variety of choices (although most places do not stay open till late in the night).
Places to stay: (historical) downtown is not far from LNCC, but it's not within walk distance, and there are buses serving the area. There are plenty of hotels in the area for the visitor to choose from, and I'd suggest checking the Petropolis pages above and pick your favorite. For a longer stay, (one month or more), there is always the possibility of renting an apartment at the Quitandinha, at quite afordable rates. A list of hotels follows here and here.