A few years ago a bunch of ChefTalk folks got together at Chelsea Market, which is now the home of the Food Network. Can't promise any celebrity sightings

but just walking around the market is great fun! There's a wine shop, several bakeries (including Amy's, which has its production facility in full view), the production facility for Hale and Hearty (the soup chain), Ronnybrook Dairy retail (get the ginger ice cream

), a butcher, fishmonger, Manhattan Fruit Exchange, a Thai grocery, smallwares, and Buon Italia, a terrific Italian grocery. And it's located in the newly-trendy Meat Market area, where there are lots of fancy shops (good for window-shopping) and restaurants (people-watching).
From there, you can take a crosstown bus to the Union Square Greenmarket (open Monday, Wednesday, Friday, and Saturday). Even at this time of year there are lots of vendors with lots of great stuff to look at and talk to them about.
As for pizza: check out
Time Out NY's recent articles. A lot of my friends prefer DiFara's, some really like Franny's -- a trip to Brooklyn in either case. I was disappointed in Grimaldi's on Old Fulton Street, but the search goes on!
Enjoy your visit!