In a capitalist system, this shortage would cause hospitals to raise their pay and attract more doctors and nurses. But since Medicare and insurance companies decide the reimbursement rates, that can't happen, at least not for as long while until new contracts are negotiated. Since most people get medical coverage through their employer, we can't even have insurance companies competing directly for our business. We may not have fully socialized medicine, but we most definitely do not have a capitalist system either.

I wouldn't bother driving to NYC. Boston is much closer and would be just as fun for a tourist IMHO. Meredith, NH to Manhattan would take you a minimum of 5 hours of driving, plus traffic.
As others have said, weather conditions can change quickly, so I'd recommend shorter hikes with flexible clothing that you can add or subtract layers depending on the conditions you run into.