The next day we ran madly about town (whose idea was that), running errands, finding train stations etc, etc. We managed to book a train to Agra and a train to Varanasi. We also stopped at India gate and had our photo taken with groups of Indian tourists.
We sat on the street at dawn and drank chai, and lo, we were not harassed. For a full hour or two. Oh, and we tried our nasty mcnast aquatabs, in an attempt to use less plastic bottles. The verdict so far? Undrinkable.