East Beach for winds from NE through to SSW is sort of "the" spot most newer riders go to practice. It can get crowded.

I have ridden where you were today on SE winds.
It's actually really nice once you get away from shore. Weekends is usually pretty crowded on the "beach" itself, as you noticed. I don't think I would consider going where you were today alone due to the powerline/road hazard.
With an instructor (especially if he got you out onto the grassflats in front of the powerplant) that's a good spot to teach at with particular wind directions, I would think.