Note that many of the summer fruits and veggies that fluffians like myself enjoyed over many many years, came from Jersey - blueberries do well, tomatoes (of course), corn, peaches - much of this coming from South Jersey.

You should still be good with all sorts of things including what I listed. You can make a nice bed for the summer veggies in the sun and even try grapes. You can grow strawberries in sun or part sun. Also fruit trees like peaches, pears, apples, cherries, and plums. It all depends on how much work you want to go through to prepare for what you want to grow and also guard against the critters that might eat your harvest before you do (ie., deer, racoons, squirrels, skunk, ground hogs, rabbits, chipmunks, moles, voles, and even Canada geese - which I noticed seem to hang out in North Jersey 'burbs...lol). :-) This means you may want to consider fencing, netting, and other deterrants as part of your planning.

Fruits:
Blueberries
Raspberries
Blackberries
Strawberries
Mulberry trees

Overwinter-able veggies:
Spinach
Onions
Garlic

Spring/Summer/Fall veggies:
Tomatoes
Peppers
Broccoli
Cauliflower
Carrots
Lettuce
Radishes
Turnips
Watermelon
Muskmelon/Cantoloupe
Squash
Green Peas
Beans

This is what I've grown successfully, and that's pretty much all I've ever tried. Basically, in zone 6 NJ, you can grow pretty much ANYTHING, except citrus and tropicals perhaps (even with some exceptions).

Welcome to the Garden State!

Dave NJ

As Dave said - welcome to the "Garden State". :-)