I was there last Saturday to see the Matisse exhibit and since it was an all-day stay at the Met I spent time in the arms & armor exhibit. All I can say is don't plan to go there on a Sat or Sun, the whole museum was wall to wall people and it was hard to get close to anything or observe exhibits with ill-mannered people passing right in front of you while you're viewing. Since it was so crowded, this got to be extremely annoying. I would go on a weekday morning.
Here are the hotels around the Met. Google each to see what they have to offer in terms of restaurants and coffee shops.
http://www.tripadvisor.com/LocalMaps..._Art-Area.html
PS: This museum in central Mass. has a very fine collection (click on "collection").
www.higgins.org/