I have little to add to Els’s thorough review (and thorough “seeing” of the site – more so than ours!) but our experience of parking might be of use. We visited on a Sun 1 Sep 2013 i.e. a “Fountain day”. We arrived at around 12.30 and parked on the access road behind the Hercules. Things were well organized with stewards present to control traffic – the entire length of that access road (shown as K6 on Google maps) is given over to parking on one side with each car directed as far forward as possible and, at that time, we were perhaps 300 metres back (the actual car parks were already full). From what we could see when we departed later in the afternoon, cars arriving after us must eventually have reached all the way back more than a kilometer i.e “Busy” but not “impossible”. But you would want to arrive some time before the start anyway.
I would also suggest that it is worth viewing the “show” in the sequence from the very top downwards when it starts at 14.30. There is plenty of time to walk down and see the “Grand Cascade” in its full glory before the water there is turned off and the display moves on – and that way you will hear the “musical statues” near the start! As the Nomination File states, “the course of the water is interrupted by three oval basins spanning the entire width of the Cascade. While these fill up spectators of the water displays get the chance to catch up with the water and get a head start on the way down, only to have the water’s roaring come up from behind again on descending further”