Where should I go next for a duty station that is on the east coast and is generally a good place for family?

Lots of options depending on your situation and family needs. What kinds of amenities nearby would be ideal? How old are you kids? Do you need good public school, healthcare, outdoor access? et.

Korea for 8 months, that does not sound correct, that’s the first thing you should change. Choice of assignments is a loose term. That is competing with several other groups who are afforded the same possibility, possibility being the operative word. If you really want the coast, and decent family life better than most installations look for a position near Virginia Beach and any one of the several bases within 5 miles of Washington DC. There are a very broad array of units with many positions for your MOS.

The cities and towns are full of safe places to live and raise children. Also many opportunities for promotion and great training.

Not really on the East Coast but—

Elgin AFB has slots for 68W E5s. It’s right next to Destin, FL—absolutely prime location.

Also consider going to an MTF if you haven’t already. Look to get promoted while in Korea and then try to get a Clinic NCOIC slot at Ft. Belvoir. You want a broad base of experience when going before the E7 board.