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Looking at the map of Con Dao, there is a small airport there and according to flightradar24, there are flights from HCM and Can Tho.
I do NOT recommend going to Nha Trang.
I was there 2013 for the first time, then went back 2018. Oh my how the place has changed in just 5 years. Crowded, loads of Russians and loud Chinese tourists, and it was just noisy!
Been to Phu Quoc as well. Was in the Vinpearl resort. Very clean, lovely quiet beach. It's also got a waterpark and other activities/amusements. Not sure if worth the money though.
One place I would highly recommend is Mui Ne. It's a small resort town not far from HCM with a long strip lined with palm trees. Good for surfing. Quite evenings but still have the bars, shops, restaurants and the seafood of course. There's mud baths and spas also. A few miles north and you're at the white and orange sand dunes and lotus lake!
Check out some of the photos here.
https://www.google.com/maps/place/Mũi+Né,+Phan+Thiet,+Bình+Thuận+Province,+Vietnam/@10.9604389,108.3107692,11z/data=!4m2!3m1!1s0x31768e4c7f7c96b5:0x1a406b72c1020724
The wife is from Vietnam so I've been there a few times now. Singapore is also bloody amazing if you're in that part of the world (my favourite country now ) but you should probably leave it for next time.
Mui Ne is 'Russian world', but I agree, I like it too.. not sure I would go there if I didn't live here though