Travel to Another State to Keep Job

I accepted a job where the company requires me to be in Newark, NJ a week per month because there are no local job that fit my skill set. I kept my residence in Florida and to keep the hotel expense low, I rented a single bedroom apartment and commuted to Florida by plane. The rented apartment needs a bed, internet, utilities and some desk and chair since I work at night as well. The bed was somewhat expensive since I have a very bad lower back (disability documented) and had to buy a special bed.

The company do not reimburse for my travel to Newark but I have to be there a week per month. It's required for me to keep my job. Can I claim these on my taxes for unreimbursed expenses - lodging, plane fares and the meals while I'm up in Newark? I don't always go out to eat but go to grocery stores and prepare my own meals. I have the grocery receipts, can these be included as well?