Places to see - Bellas Artes, visual arts museum. Seems to be very popular among students, or maybe it was the exhibitions, don't know. A beautiful building, many different collections. Reasonably priced.
Cerro Santa Lucia - a hill in the middle of the city. Very nice park, easy climb and beautiful views.
Food - my experience of Chilean cuisine is not very positive. They seem to eat a lot of hot dogs, burgers and sandwiches. There are not that many options for vegetarians.
Insider Tip:Museo de la Memoria y los Derechos Humanos (Museum of Memory and Human Rights) is a must see. You really need to see it. Access from (inside the) Quinta Normal metro station. There's no admission fee, but the audio guide costs 2000 pesos and if you don't understand Spanish, you'll need it. Don't spend too much time in the first floor - the stuff that needs your attention is in the second and third floor. Especially the videos - watch all of them.