Jon , strongly recommend you use the search facility because
a lot will depend on how much time you want to spend on the river .
You will find a lot of folk like to slip in around Putney . A short cruise at 8 knots will get you to Wandsworth Bridge where you can open her up , subject to not upsetting house boats , passing canal boats , rowers , harbour masters & river police ! Remember that the Thames has tides of over 20 feet , and accompanying fast tidal streams . It can get busy around the Pool of London & watch out for fast rib rides from the London Eye to Greenwich .
A search will also throw up a few mooring possibilities such as St.Katherines Dock , or Limehouse ( or moor up to rubbish barge for sarnies & cuppa ).
Remember that upstream you can do the slow cruise to Teddington via Richmond , and downstream you could blast to " Sarfend " and the Medway .
There are a lot of truly spectacular " tourist sights " so pick a nice day and don't forget the camera.......