Normally you can moor up ( at cost ) on the Berkshire bank downstream from Leander Club for a good way. They are setting up for the Regatta so not sure these will be available.
Another good spot looks like Martens House, Willow Lane, Wargrave, which is a B&B overlooking the river with a private mooring. Good Gastropub ( St George and Dragon ) within walking distance or short taxi ride into Henley. Not stayed there myself, but on the radar for later in the season.