The falls are just a couple miles away. Years ago when Ocho was a more quaint place I walked to the falls from the port. I wouldn't do it today.
The thing with the taxis on your own deal is this - they will pressure you to do more than the falls. They will want to take you on a tour. They will be very persistent. I'd stick with the ship's offers for Dunn's River Falls. The advantage of a ship's tour is that you can leave your belongings in the mini-bus and the driver will guard them.
Please don't try to do the falls without a guide. I can guarantee that you will run into a problem eventually. The guides know where all the foot holds are. You don't. I first did the falls in 1981, when I was young and in shape. We decided we didn't need a guide and off we went. It was okay for the first little bit, but then we got in trouble and were stuck with water careening down all around us and we had no idea how to get out of the predicament. A guide eventually stopped his group and rescued us. It was quite humbling.