HUECU (default for Harvard loans) is free, is a credit union (i.e. a banking co-op), does offer cards, and you can keep it forever even after graduation on the condition that you use the account once a year (once the account is not used for a year, it is considered abandoned and any funds on the account will be transferred to the US Treasury). Many students however reported issues with setting up an account, an irresponsive customer service and other little practical problems such as short opening hours. You will need a Harvard ID to set up an account.
Metro Credit Union is also a credit union co-op, offers cards, and does not require a Harvard ID to open an account, but just a proof that you are living in the Cambridge/Somerville area (e.g. a rental agreement). It is ranked as the 2nd best credit union in Massachussets, way before HUECU. It may be problematic to make a standard international wire transfer to it, but anyway for that you would want Transferwise (see below), so no prob. If you want cash from ATMs, you’ll need to pay small fees as they lack ATMs in Cambridge (some account types will refund your fees though).
Bank of America sometimes has free accounts for students (as long as you’re fine with just online statements), and has the largest ATM network in the US. If you do transfers from abroad, make sure you make them in bulk (American banks are so bizarre, that they do charge you for incoming transfers, but not for depositing a check).
Another very good option is Citibank. They have a huge amount of branches in the US and they are open during the weekends, while HUECU is not (however, their disadvantage is that they don’t have branches in Massachusetts anymore). Still, they are very worth considering since transfers within the large international Citibank network are free, unlike for other banks (which means that you can transfer money from your home Citibank account for free). Additionally, Citibank gives you a very convenient way of sending checks on your behalf (to pay rent, fees, etc. – they simply write a check and send it for you, free of charge). They offer both debit and credit cards. It is worth getting a credit card, as with your I20 and tuition you’re paying you should have no trouble getting one, and their credit cards typically go with some insurance (useful when renting a car, e.g.), and also start working for your credit history.
American banks are really backwards in terms of wire transfers, and it is much easier to use an app for cross-friend payments, such as Venmo. For tracking of bill payments, debts, group check splitting, etc., Splitwise is really useful!
If you want to make international wire transfers (e.g. from country X to your US bank account), the best option (as of 2016) is Transferwise, which makes them effectively with very low fees. They basically hold branches in multiple countries, and instead of a regular international transfer, they just perform a national transfer within one of their branches and the target bank.