I'm short of time and am wondering how much of Vietnam I could see in 3 weeks? I'd fly into HCMC and out of Hanoi and could take an internal flight or two.
Any suggestions?

3 weeks is quite a lot of time for Vietnam.

I didn't reach HCMC but from friends who got there, things to see there include the War Atrocities museum, there are tunnels there too but they are not original.

If you enjoy drinking then, Na Trang and the infamous Mama Han drinking boat trip with the floating bar.

Further up the coast is the beautiful Hoi An. A beautiful place of colonial french architecture and a thriving tailoring centre. The beach there is lovely and not particularly crowded and the surrounding countryside is lush. 60km away is the ancient ruins of My Son related to the Angkor complex of Cambodia.

A bit further up the coast is the Marble Mountains and the magnificient China Beach. White sand, blue sea and no one around. Pop to Ho's and try the spring rolls.

Hue is the place near to the DMZ of the Vietnam war and you can go on trips there to visit the major sites of the war including genuine tunnels. There is also a temple in Hue which houses the car of the monk who burnt himself in protest, this image captured and used to plug Rage Against the Machine's album cover!

Hanoi is the home of the government and Ho Chi Minh's embalmed body, opened on a few days of the week and you have to wear conservative clothing. Hanoi is the hub to numerous intersting places to valley of flowers, treks in the mountains and also to Ha Long Bay with the marvelous loaf shaped hills projecting from the sea. This trip takes you to Cat Ba Island in the bay where you can do a number of walks.

Hotels are quite cheap at from about $6 but standards are good. Buses are also pertty good though it was bumpy when I was there especially between Hanoi and Hue as the road (one and only north - south route) was being repaired. Train takes ages but is smoother.

Hope this helps.

Hoi Ann is lovely.