There are stretches along the river where you can walk.
But I must say, as a former Saigonese who grew up in district 10; with my sister still residing there, I've always jumped on a bike to ride to district 1, so I don't really pay attention.
The stretch from Ham Nghi northward is a good. They are working on making both sides of the river more attractive and conducive to walking.
The plan is to turn ít into a boardwalk.
Nguyen Hue st is being converted into a pedestrian area (during certain period of the day at first) starting some time in May, I think - at least that's the plan, as I know it.
It will lead directly to the riverfront.