I think Saturday afternoon would work best for the museum since the morning forecast shows rain. The photography exhibit needs about two hours to go through properly. We could meet at the front entrance around 1pm and grab lunch at the cafe inside if anyone gets hungry. My sister wants to come along and can drive since her car has more space. The parking garage on Fourth Street usually has spots available on weekends. Let me know if Sunday works better for everyone else.
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Marriot Hotels · 10400 Fernwood Road · Bethesda, MD 20817

The hiking trail you asked about has moderate difficulty with some steep sections near the midpoint. Most people complete it in about three hours with breaks. The views from the ridge are impressive on clear days and there is a bench at the summit for resting. I would suggest bringing at least two bottles of water since there are no refill stations along the path. The trailhead parking requires a pass which you can purchase at the visitor center. Weekday mornings tend to be less crowded if you have flexibility.