Does a jaunt around the local area with a landing at two local fields in class G within 50nm require a flight plan?
No, not as I understand it! (Sorry, I am too old and been doing it too long to to bother quoting regs).
and those flights intending to operate in controlled airspace other than Class E MUST...
Again, can't quote the regs - but operationally that is not so, although you may get a clearance a few minutes faster if you do. On the rare occasions that I leave or arrive at TL VFR I usually don't submit a plan - just call up TL Clearance Delivery with details and request.
Dr
PS: When they stop changing the regs every 5 minutes I may take the time to learn then off pat again!