OP: the canal is great. I used to run it daily as a commute to work in Rosslyn. I miss running the C&O.
If you're staying near the Mall and want mostly soft surface, you can park under Whitehurst Freeway near the Georgetown side of Key Bridge. I imagine you'll be going early, so you'll be fine parking-wise. If you don't mind driving a bit, you can go up to the other areas like Chain Bridge, but it will cost you time.
You can also park at the Georgetown waterfront and just run behind the M Street Stores until you hit the canal. If your hotel is close enough to Georgetown and you are running in the AM, you might even be able to just run there.
When we're back in town, we usually stay in Foggy Bottom or Dupont and I just run from the hotel.
Enjoy!