One of my favorite places to go boating is on the Intracoastal (Palm Valley/Nocatee area) and head south to St Augustine. Here is one drop off point for your boat.
From the Avenues mall, go south on Phillips Highway, turn left onto 210, also know as Palm Valley road (by the Gate gas station). Palm Valley road turns into Nocatee Parkway. Keep going, you will see a bridge, go over the bridge, at the bottom of the bridge turn right and follow the road around. You'll see the boat ramp.
As you can see the waterway is beautiful. If you head south towards St Augustine, you'll actually make your way to the Historic area of St Augustine, by the Bridge of Lions, which is currently being restored.
As you make your way towards the Bridge of Lions, you can turn left a little before the bridge and head out to the ocean.
And since the ocean is right there, if you watch the waters, you'll see dolphins swimming in the Intracoastal.