Fees and finances
Most students can expect to pay about $700 per semester in mandatory student fees (more for international students depending on nationality). These are due on September 15th and February 15th for the fall and spring semesters respectively, although they can each be split into several pieces, to be paid throughout the semester using the Time Option Payment Plan. Additionally, there is a fee of about $100 due early in the summer. If at any point your expenses are too great the Stony Brook Graduate Student Organization (GSO) offers multiple forms of financial assistance, including emergency loans that are extremely useful and recreational reimbursement for such things as train tickets or concert tickets for any activities in which you may like to participate in the city.
If you will be a TA, you should be aware that you are paid over two-week pay periods, at the end of the following pay period. That is, you may not be paid until up to four weeks after you start. Do not be afraid to take out an emergency loan from the GSO or to ask to borrow from someone around you.
If you intend to get an off-campus apartment, you will probably need to pay two months' worth of rent when you sign the lease: the first month's rent plus a security deposit.