I've done the loop around the island in my canoe, and most of the water wasn't very exciting - most of the shoreline is shallow and muddy and, often, gross. If you do check it out, I'd spend most of my time around the rocks at the north/upstream end of the Virginia-side channel, right in between the footbridge and the Key bridge. At low tide there are a bunch of rocks visible, at high tide you might have to work at finding them. After that, I'd float downstream and fish around the pilings.
As for put-in, there's a parking lot off of the GW parkway on the north side, would be easy to put a kayak in.