Air conditioner efficiency is listed on the side off all units as a number called the EER (Energy Efficiency Rating). The EER is a simple ratio of the BTUs of the unit to the amount of power it consumes in Watts. Thus an air conditioner with 10,000 BTU capacity and an EER of 10 consumes 1000 watts of power -- which is a lot.
The government mandates that all window units have a EER of at least 9.0, but there are plenty of well-priced units out there today with ratings of 10.5-11 to be had with a little bit of looking. These more efficient units will also have an Energy Star label on them because they exceed the minimum standard (9.0 EER) by at least 15%.
The more BTUs or the higher the EER, generally, the higher the price of the air conditioner. However, since most people buy over sized air conditioners (too many BTUs for their purpose) and often don't look at the EER rating, it's possible to both save money on the up front purchase and reduce your monthly electric bill by getting the appropriate sized unit with a high EER.
And remember to keep the thermostat at something reasonable. You're not trying to turn your apartment into an icebox, you're just trying to take the edge off the heat and humidity. If your AC has a timer feature you can use it to cool your place before you get home, but remember that an appropriately sized air conditioner will cool a room pretty quickly.
If you live in drier climates, evaporative cooling may be an alternative (and more energy efficient) means of keeping cool worth looking in to.
For a list of the most efficient window unit air conditioners see the American Council for an Energy Efficient Economy.