I'm a born and bred Boston guy (just south of the city now) and lived in NYC for 5 years. Lots of good suggestions already. In NYC, I always liked Peter Luger's steakhouse-very old school experience, cash only. In Boston, Gummi/Laurence gave plenty of good suggestions. I'll only add one of my favorites, which is the original Pizzeria Regina in the North End. The North End itself is a great place to walk through and see all of the restaurants (Modern over Mike's for the pastries though). Beantown Pub is a good place to people watch and have a pint or several. I work a few blocks away from there so let me know when you are going to make that stop on your adventures.
You could probably fund some of your trip filling your checked bag with Aussie only Weber products and accessories and selling them here!