River Buses
The Thames isn't entirely unused since the demise of the age of the great London docks - there are now a number of river bus services available for you to travel up and down the river, and also numerous tours and cruises.
Holders of a valid Travelcard can get a third off fares (note: One Day Travelcards are not valid until 0930). I've twice taken the City Cruises route from Westminster to Greenwich; each time cost me £4 (with the aforementioned discount) and was a pleasant 45-minute journey. Until Tower Bridge a "funny" commentary was provided by one of the boat's staff regarding visible things and places of interest; I hadn't expected it. I had, at first, imagined that it might be different for every boat crew, but both times I managed to get the same guy doing the same commentary, word-for-word. Good luck avoiding him.
There are various different models of boat doing the rounds; on some the bow of the boat is open-air benches, whilst the cabin at the rear has a bar with drinks and (pricy) food. Others have the open-air seats at the back, on the roof of the cabin with the bar. Others still are fully enclosed, but that's no fun. Not that I would ever espouse such a thing, but conceivably the open-air seating areas on these boats would be a lovely place to smoke a nice spliff, especially on a nice sunny day. Remember to dress up warmly, because it can be pretty windy whilst whizzing along in the open.
Fares, timetables and a route map are online at the Transport for London site, along with general information about services.