Do a little research on microclimates. Of the places you listed the worst one would be in a depressed area (low spaces tend to collect cold more than raised places. If possible you will want a south facing wall (preferable with full sun) as this will give you the best natural position, though you will likely still have to protect.

Brown Turkey is probably not a bad choice, but there are figs reportedly more hardy or who are more likely to produce if wood is frozen back or otherwise damaged.

Welcome to the forum, you'll find we're a good group (and if you ask during the right time of the year many here will likely even share cuttings with you of some of those more desirable varieties for us northerners).

There are a number of NY and (especially ) NJ posters here (though I am not among that number)

~Chills

Sounds good! Yeah I do have one location which is up near a south-facing brick wall and has a narrow brick walkway nearby- should be an ideal spot for heat radiating from the bricks...

My soil here is rather on the clay side. The soil is thick very few rocks. Any suggestions on what to amend the soil with for figs? Should I add rocks? sand? lots of compost?

Well, yesterday had a frost warning so I didn't plant yesterday. And looks like tonight is another frost warning.

The trees are still sitting in the boxes they shipped to me in. I just opened up the boxes and removed any padding inside for their shipping so they can breath.

Is it OK that I have had them for almost 3 days now without planting them in the ground yet? I am keeping the box outside during the day in a shaded area, then I bring it inside to the garage for night.

Tomorrow's low looks like 49 so I'll finally be brave enough to plant them tomorrow!

Trant
Keep the roots moist and away from sun and dessicating air and it should be OK for a while (and more so with fig).