cheap, casual on the UES?

my little chowpup has started school on the upper east side, and i really don't know the area. i'd love your suggestions for casual fare--good coffee, pastries, breakfast sandwiches to grab after we drop her off; casual, child friendly places for a bite after school; ice cream/gelato better than the soulless stuff we already got at ciao bella on day one.

prefer good price to quality ratio; it doesn't have to be cheap, but it should be worth the $/calories. good vegetarian options preferred (but not necessary for all of us). geographic parameters around 86-103rd, lexington to the park.

thanks so much in advance!