Greenwich makes sense as a walk and nothing else. The observatory, the ships, the tunnel under the river, the sudden turn toward the dome — it's a five-kilometre line that covers four centuries.
Start at the top. Climb to the Royal Observatory, stand on the meridian, say the thing about zero degrees out loud. Drop through the park past the Queen's House and the Painted Hall — both worth stopping at, though only the Hall is worth the ticket.
At the river you get the Cutty Sark, which is less hokey than expected. The foot tunnel is free; take thirty seconds to walk down the spiral stair and feel the shift of air, then come straight back. Don't cross.
The last stretch is the strange one. You walk east along the Thames Path past the power station ruin and the wharves, and the O2 dome looms up looking like it shouldn't be there. Get there at the hour and the cable car's moving overhead. End in the plaza; jump on the Jubilee line.
