Let me just suggest you stay away from those small little hydroponic herb gardens you see on TV. You know, the one with the huge light? My mother bought one of these, and they work fine, if you only want to use your herbs once every 3 weeks.
Growing herbs inside with low light will generally get you some stringy lanky looking herbs. They will be reaching for light and producing sparse leaves and low oil content.
Outdoors is the way to go. Herbs will do just fine, even facing east. Where I live, I put some out on my porch facing east:
They get sun there for about 6 - 8 hours during the spring and summer, depending on the time of the season. As you can see, they do just fine there.
I grow more herbs just out of the shot view of this pic where there is full sun, but the ones on the porch are really close to my kitchen, so I can grab them when they are needed without trudging to the garden.