Even in a big city like Ho Chi Minh, it's easy to find local scenes. You just need to leave the tourist areas of district 1 and head out to somewhere like Binh thanh or district 9 or 12. You can get a bus out there from the bus station near Ben thanh market I think. We used to live next to ba chieu market in Binh thanh and it sounds like that's what you are looking for.
As for traveling, the most popular way to travel south to North is either on the open buses, where you buy a ticket and then stop off en route at chosen places, or the train, which works in a similar way. However, if you do this, you are not really going to be able to avoid the touristy parts. Don't discount flying, as there are some really cheap budget airlines like Air Asia and Vietjet air and it will save time as the journeys between places are big.
From Ho Chi Minh you can go to the Mekong and stay in a homestay. The towns along the Mekong are mostly very non-touristy. Tour buses come in and leave again but you could stay there and avoid those crowds.
Do you want to visit beaches? Mui Ne is very touristy but Phan Thiet, the nearest town, is less so. If you go last the main strip in Mui ne you get away from the crowds.
If you don't fancy beaches I would recommend you fly to Hue. The old city and tombs are very interesting. Then you can travel over the Hai Van pass to Hoi An. You can do this by motorbike if you want, with a guide, and the views are spectacular. As a photographer I wouldn't miss Hoi An, touristy as it is, because it's stunning.
If you didn't want to fly, you could travel from hcmc to dalat in the mountains. You can do a tour with the Easy Riders where they take you on their bikes around the countryside. You can negotiate with them what you want to see.
Then I'd fly to Hanoi. From Hanoi you can visit Ninh Binh to the carsts, and Sapa. Instead of doing a halong bay tour, I'd get a bus from Hanoi to Haiphong. It's one of the biggest cities but not really on the tourist trail. We used to live there so check out our blogs on it. From there you can take a ferry to Cat Ba island in Halong Bay, which is more of a Vietnamese tourist resort. You can arrange people to take you in a boat trip from there, and tour around the island. There are some home stays there outside cat ba town.
Instead of sapa, which is very touristy, you could go to a different mountain town. Tours can be arranged from Hanoi.
Don't worry about the tight budget, there are rooms to be had for about $7 a night, especially outside the tourist areas.
Have fun!
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