DirecTV's page says my Azimuth angle is 228. I'm guessing that measures 228 degrees from due north, but in which direction?
That's correct. You should measure this angle clockwise from North.

I'm just concerned about finding a good place for the dish, I read that putting it in a window can cause problems

There is a special polycarbonate material I read about a few years back that has a significantly lower signal degredation characteristic than glass. Due to the inconvenience of having the dish indoors and the likeliehood of needing a larger dish to compensate for signal loss it is not a popular alternative.

One thing that may help you is to drive around the area and look at where other peoples dishes point to get a feel for where you would need to point yours.