Yes, you can. The banks are pretty steep here though. You can also walk, jog, run, or bike on the city maintained trail that runs right beside the park and portions of the river.
It has a great bike and walking trail , there is a bridge that goes right over the flowing river. That trail is a great feature for Riverside Park, the campground has the River running right behind it, the banks are steep. If there are fishing banks you would need to ask a local. I don't fish when I visit.
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