Hey! So the way I get there is by way of Riverside Drive along the South side where it passes under the Train Bridge. I ride my bike and just lock up to a tree so I really don't know where if anywhere you could park a car nearby. There is a 'trail' down underneath the bridge but you have to cross the tracks and it is clearly marked no trespassing. The bank past the tracks is fairly steep and once you get to the water you pretty much have to wade out to the good rocks/islands in the middle. I only like to go when the water is about 5 feet or lower - you can check the official current and forecasted levels here: https://water.weather.gov/ahps2/hydrograph.php?wfo=akq&gage=RMDV2

I definitely recommend checking that site before you go anywhere on the river. I've seen it rise at rates of a foot or more per hour and it's very hard to notice unless your bag starts to submerge.

Another possibility is Pump House Park North side in Byrd Park, which has parking and is much easier to get to. If you cross the bridge and take the short trail along the canal it eventually leads to a hole in the fence (also likely trespassing but people cross the tracks there all the time). Across the tracks there are trails both ways along the river so you can get under the train bridge this way too. The problem with the North bank is the deeper channel runs closer to it there so you can't really access the same areas without essentially swimming as far as I'm aware. There are however some other great rocks/islands accessible on that side (again when the water is low), they're just a bit downriver from the Train Bridge.

Sorry if my directions are a little long-winded. If you can't tell already I also have somewhat of a strange fascination with that bridge - It's my favorite spot in Richmond by far. If you're interested in some tips on accessing the top of it I'd be willing to talk about that as well. I've been up there quite a few times and the view is spectacular, but it's obviously not something I'd ever really condone especially to someone I don't know due to the risk involved.