Yea check the alternator first I've had one go bad and not turn on the battery light recently. If you have a multimeter you can check it youself.. just measure the voltage at the battery with the engine running and you should get 14.1 - 14.4 volts DC or so. If it's down around 12v or less you have a charging system problem.
If that checks out ok then you will need to check for a parasitic draw.. once again you'll need the multimeter. Disconnect the positive battery terminal and connect the positive lead from the meter to the cable, and the negative lead to the battery +. Set your meter to measure amperage and see what it says. It should be well under 1 amp of draw if everything is normal. If not, start pulling fuses one by one until you find the one that drops the current draw and you have found the problem circuit.