Went there for 16 days 3 years ago. Absolutely incredible place, you won't be disappointed.
Days 1-3: Airbnb in Hanoi. You can Uber everywhere (use it from the airport as well), Street food is amazing (Pho, Bun Cha etc), had it every day. You can see which ones you can 'trust'. Visited all the main sites/attractions. Mostly walked (when you cross a road, do not hesitate, just GO and you will be fine). Book a street food tour on your first day (gives you a great feel of the city). Take a private cooking class (they take you to local markets and you then prepare some of their most iconic dishes). Enjoy the coffee and the shopping!
Days 4-5: Booking.com on Cat Ba Island (southern part of Ha Long Bay). Book your transfer before you arrive (bus to Haiphong Port, hydrofoil to Cat Ba). From friends/reviews, it is much better going this way than staying on one of the Junk Boats in the Bay for a few days. On Cat Ba, go for a hike with a guide on one of the larger island. Go kayaking in the bay between all the islands (breathtaking literally). Also do rock climbing which it is quite famous for.
Days 6-14 Head back to Hanoi. Catch a flight to Dong Hoi (lowest cost airlines available, same price as ours). Get a transfer to Phong Nha. I stayed at a Airbnb. Easy Tiger is the alternative. It is a massive hostel with an amazing setup. I spent most days there but then could retreat back to my own place. Rent a scooter for the whole time you there (super cheap) and just explore. Visit some of the worlds largest caves ('Paradise Cave' is fantastic). Do jungle treks and swim in rivers inside massive caves ('Dark Cave'). Hop on your scooter and ride around Phong Nha National Park (one day I rode to the border with Laos). Visit the 'Pub with Cold Beer' where you, if you like chicken, grab a cleaver and have the honors...
Day 15-16: Back in Hanoi. Flew out with Cathay. Alternative is Singapore Airlines, otherwise look at the ME carriers.
I know many people want to do the whole of Vietnam in one trip, either from Saigon to Hanoi, or vice versa. I don't suggest this as you will just end up rushing through everything. Yes you can rent bikes for next to nothing. In the rural areas I felt confident (former Enduro rider), however in the cities it is chaos.
If you in Hanoi and want to enjoy the surrounds, consider Sapa (mountains, very rural, go via train) and Cat Ba (island life).
If you willing to venture south, Phong Nha is great for jungle adventures. You can also visit Da Nang for a beach holiday. Hoi An and Hue for a cultural experience.
Many people travel via train internally. If you strapped for time, i suggest just flying. The airlines are good and they are cheap.
Any questions, let me know. I can share some pictures in the next few days.
