Rock Creek offers shade and several water/bathroom opportunities:

Go from Iwo Jima down to Memorial Bridge.
North along Rock Creek Park Trail past Watergate, Georgetown.
At 4.2 miles out, stay on the main trail and go around the tunnel, not through it.
At 5 miles out, trail passes the Zoo entrance... water 50 ft inside, bathrooms in the zoo, pandas a half-mile up the zoo hill.
Continue North along the bike path.
At 6.5 miles out, at Peirce Mill, water fountain on trail and bathroom stop to side.
Just past Peirce Mill, trail passes a parking lot, crosses a road and empties out onto Beach Rd, which is closed to cars here on weekends.
At 8.3 miles out is the Park Ranger Station. It is rumored that there is water across the street.
Turn around and head back here for a 16.6 mile run, or...

To get to the Beltway, continue on Beach Rd., but this may be over 24 miles round trip.