I was in Vietnam in January this year on my own (retired woman). With 10 days, I'd choose 2 cities. Fly between them - there are cheap flights on perfectly acceptable airlines and fly open-jaw, into one and out of the other. Once you see the traffic, you will understand why everyone says do not rent a car. Riding a motorcycle is completely unsafe without a passenger, way too suicidal with one. Sometimes I felt like I was living dangerously just crossing a busy street. The best way to do it is to adhere to a local. Do not trust traffic lights, apparently they do not apply to the myriad motor scooters and are often just a suggestion for car drivers.
I stayed in "old town" central locations in both Hanoi and Saigon and never felt unsafe. There are lots of locals out and about until the late hours. I stayed at the Boss Legend in Hanoi, on the edge of the Old Quarter, very interesting area, walking distance to many sights. It's modern and very comfortable ($75/night, good breakfast). In Saigon, I stayed at the Papaya Saigon Central (double room for $75/night, lousy breakfast but who cares at that price), about a block from the night market and walking distance to many sights. Staff at both hotels were very helpful.
I got a VOA (visa on arrival) very easily. I used this service. Here's how it works. You get a "visa approval" letter by email and print it out. (I got mine in 2 days). Also print out the visa request form (don't remember where I found it online - maybe that website) and fill it out. You can get forms at the airport, but it slows you down. When you land at the airport, you take the letter, the completed form and passport photos and your passport to the desk. When your visa is ready (15-30 minutes usually), they call out your name (often mispronounced) but also your photo and name appear on an overhead screen. Then you pay - it was $25 then, must have cash dollars. And you're done! Caveat. This may not work well if you are flying into Saigon, since it's a very big, busy airport and lines for the VOA can be long. I flew into Hanoi and it took me less than 1/2 hour.
While the cities are very interesting, my best days were those I spent away from them. From Hanoi I took a 2-night trip to Halong Bay (there are also 1-nighters) that can be arranged at low cost from local tour operators. In Saigon I took one day trip down the river to the Mangrove Preserve. In the past, I'd taken a day trip by boat to the Mekong Delta.
To get around the cities, either walk or use Grab (it's just like Uber). I didn't have a smart phone with me, but the few times I needed a ride, my hotel or the restaurant I was at called one for me.
If you have any questions, please feel free to PM me if I don't respond to your thread.