Many of the high moorland 'circles of Britain, where the stones barely break the surface, make it abundantly clear these were purely functional sites, the builders in awe of their surroundings and making no attempt to compete with nature. Castlerigg may be a photographer's wet dream, but I think, for example, the Burn Moor 'circles are actually the real deal instead.
To answer the 'upon arrival' bit, my first thoughts are often... 'is that it? stones aren't that high etc..' But first impressions, in my experience, are often very mis-leading.... just scratching the surface. My average visit time, I'd say, is about three hours.. sometimes longer if the vibe is really there, sometimes shorter if access is an issue. But I find it takes a while for the relationship to the landscape to become apparent, to try to understand why the monument was placed where it is. Very often the attention to detail with regards placement is astonishing, almost as if the form of the site is very much of secondary importance to where it is. Dunno, but in my view if you don't take the time to sit, look, absorb and think, you may as well be collecting stamps for all the insight you'll get. Less is most definately more.
Sometimes also walking to a site helps to raise appreciation; for a long time walking to West Kennet Long Barrow from Avebury was my favourite walk ... always sitting at the end of the barrow for a good while listening to the skylarks and watching the clouds. One time I took a day off work and went over there mid-week, I was completely alone until a wren flew out of the barrow and sat a stone for a bit.
More recently the walk to Boscawen-un from St Buryan heightened my appreciation for the place. There were a couple of women sitting in the centre of the circle when we arrived so we just sat discreetly outside the circle and waited until they went. I think we stayed for about two hours, people came and went while we just sat still and I know I took the spirit of the place with me when we left.