From Hanoi you could take a short VN flight to Vinh if you fancy seeing what East German post-war reconstruction looks like. Flight is 40 mins (on a Fokker jet) to one hour (on an ATR72). Or there's Dien Bien Phu if you're a military history buff.

From Saigon, there are more and better options all around the south - Nha Trang is Vietnam's "resort" city, Phu Quoc its resort island (and not that developed - yet), Con Dao for the best diving in Vietnam, etc.

In a weekend it'd be easy to pick up four or more segments by hopping around on VN. Quite a few airports are long drives from the town centres though (but not SGN, which can be done in under ten minutes when there's no traffic, and more like 25-30 when there is).