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Staying closer to Georgetown lets you easily get out of town by Macarthur Blvd. Once on Macarthur, you're on the main path out to where people ride. Go out to Angler's Hill and Great Falls, and from there onto Falls road out to River, and from there you have a ton of routes at your disposal.
There is also the option of lunch rides at Hains Pt (East Potomac Park) which are quick and generally organized (my right tibia may disagree with me on that) and in the shadow of the monuments. I don't know how cherry blossom season timing works this year but avoid Hains in peak cherry blossom season.
If you bring a gravel bike, you can go out the C&O Canal for miles and miles, and then hit the Blockhouse Trails out by Lock 22.
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