I would say alternator too. The cheap mans test is to start the car put on the headlights(and other electrical) and then disconect batery terminal(Negative, carefully) so the car is running purely on the alternator. If the lights dim down when battery is removed the alternator is not making sufficient power.
Although that use to work on older vehicles before the invention of the on board computers. I would strongly advise AGAINST doing this. What happens when you do that is the altenator sees zero volts coming in and immediatly full fields the altenator which is okay after it stabilizes. However in those few short moments before it stabilizes it can deliver a voltage spike that is capable of frying your computer.
The only correct way to do it is to either have a battery/altenator tester or just use a volt meter and make sure it's around 13.5 volts+.