When I take a temp administrative job on a college campus for 3 to 8 months and they provide housing, are my trips home on the weekend tax deductible?

If you are self-employed and have created an LLC, you file your business income and expenses on Schedule C - unless you elected to be taxed as an S-Corp.  If you are using Schedule C, you would include your travel expenses as business expenses on Schedule C.  There is no need to treat it as a reimbursement.  If you have chosen to be taxed as an S-Corp, then you would want to report the expense as business expense on your Form 1120-S.