Just up the street from the Met.
5th Avenue and 86th Street -
http://www.neuegalerie.org/Great collection of Austrian and German art and a really great cafe on the first floor.
Also, any of Danny Meyer's restaurants - Union Square Cafe or Blue Smoke..
If you're coming to Philly, eat at Standard Tap, 2nd and Poplar - about a mile from the Liberty Bell.
In Old City try Mandoline - a BYOB on Chestnut Street bet. 2nd and 3rd (dinner and cash only), Tony Lukes at Front and Oregon in South Philly for the ubiquitous cheese steak or Italian roast pork sandwich with Provolone and broccoli rabe. And ignore the Hard Rock Cafe at 12th and Market and go into the Reading Terminal Market at 12th and Arch instead. There are some fabulous small merchants there who do great stuff for lunch. Buy your sandwich or whatever and go into the Beer Garden in the center of the market, and have a beer.
VietNam Palace on 11th Street between Race and Vine has amazingly inexpensive and tasty food.
If you want really cheap go to the Hand Drawn Noodle House on Race Street between 9th and 10th. Cash only and you'll likely be the only Anglos in the place. Order the Fried Soy Sauce Noodles and watch the chef make the noodles in the kitchen.
Try the Rodin Museum on the Benjamin Franklin Parkway for the biggest collection of Rodin outside of Paris. If you want something bizarre go to the Mutter Museum of medical oddities. And if you've got the time go just outside of the city and visit the Barnes Museum on Latches Lane in Merion, PA - 5 minutes outside the city limits
http://www.barnesfoundation.org/r_main.htmlYou want more restarants or sights in Philly, let me know.