Its surprising to think you can live somewhere for years and years and not realize how close you are to a place as beautiful as Great Falls. The park had a $10 fee per vehicle, but it was well worth the cost. Just a short walk from the parking lot is the overlook, which has amazing views of the river, and then you can take your pick of multiple hiking trails along the river.
It gets very crowded in the afternoons, but at 9am in the summer it was practically empty. As fall is beginning, I'd say its a great time to go. Make sure to bring everything you need for hiking if you decide to do more than just the path to the overlook. The Billy Goat trail is the most rigorous, and the longest, and much of the trail is covered with rocks so good hiking shoes are important.
I'm hoping to try out the Virginia side soon, but I've heard from friends that it isn't as well up kept. I'll let you know how it goes!