You should have no problem getting to rural tourist destinations from Hanoi, although the tourist destinations will likely not be that rural in a traditional sense. Halong Bay is amazing and the coastal area in that region is worth checking out, although there are a lot of tourists and tourism infrastructure which slightly spoiled it for me. Great place to take photos, though.
One of my favorite places in Vietnam is Sapa, in the far Northwest. If you cross the border from China you will probably pass through this area, but it is far from Hanoi. It’s all picturesque rice fields and mountains at pretty high altitude if I remember correctly. Fantastic place to rent a motorbike and explore (and that is the best way to get around Vietnam in general aside from long trips).
Have fun, Vietnam is beautiful. Look out for people trying to rip you off – they are everywhere.