I'd calibrate at the TV. The BDP-83's default values are quite accurate, so leaving them alone should give you a very good input to the TV.
Certainly calibrating to compensate for any consistent errors from the box would be handy. I see a couple of problems with trying to do this calibration, though. First, getting the test patterns. There may be some providers that run some patterns on a station hidden away in the line-up, but my provider never has as far as I can recall. Even for boxes that have an input and can pass through a signal, the signal path is likely to be different enough that it wouldn't be a useful metric for calibrating. Second, the source material itself can be suspect in some cases, even moreso than with DVD (although badly authored discs are always possible). The first time I really properly calibrated a TV with a Video Essentials DVD, I switched over to the local news afterward and was horrified to find that the reporter "on location" somewhere in town looked to have a dreadfully orange tan. I double-checked my calibration, then went back to the local news. I flipped through some other channels and found that the problem was with the news broadcast itself. I'd expect many broadcasts to be reasonably accurate, but there will be more variation.