I'm a huge fan of Vietnam, and I've been there several times. My favorite way to experience it is definitely the traditional way: by riding a scooter on the back roads. You can see so much more that way, and you really get to interact with the people in a way that you can't if you're just driving through in an air-conditioned car.
I also love going on a Buddhist pilgrimage! It's such an immersive experience, and it really gets you in touch with your spirituality. I know that sounds cheesy, but if you're looking for something more than just sightseeing, this is a great option!
And lastly, if you're looking for something off-the-beaten-path, try renting a boat and exploring some of the smaller islands off the coast of Vietnam. You'll meet some great people who live there and have access to some incredible food that most tourists don't get access to (for example: fresh squid!).