Apartments: If you live ON CAMPUS (dorms), in some schools you have to pay extra to stay in your dorm during semester breaks. In some schools you even need to move out and can only get back into your dorm after the break. Check it out before you move in to prevent unpleasant surprises.
Tax & tips: In the US you tip many people for many services. You tip waiters, barbers, taxi-drivers, delivery people and many others. In restaurants you should pay 15-20% of your bill as a tip.
Another unexpected cost hides in taxes, which are usually not included in the prices in stores. This might be annoying, and also hard to remember. You may be surprised when you get to the checkout counter and see that all of the products you are purchasing add up to a higher sum than you were expecting (in some states it is more than 10% of the price of the products).
Buying a bike will probably be cheaper than paying for public transportation (but tie them up well!).
Use craigslist to buy second hand furniture (but make sure they don’t have bedbugs!).
As to tax and tips, when budgeting for your time in the US, remember to add 10-20% of what you expect to spend monthly for these costs to make sure that you have enough funding for your adventure abroad.
Even when you do have health insurance (and please do), your insurance would most likely not cover the full cost of doctor's appointments, and will almost never cover health issues with your eyes and teeth. Costs of doctor’s appointments beyond what the insurance covers can be very expensive – sometimes more than $100 for a simple visit.