Hurst Castle is currently with English Heritage so if you have a membership with them it would make a great day out. Even if you don't you can still visit the castle but you have to pay. There's also a light house near the castle, which is worth taking in, for more information about the light house, the castle, and an awesome aerial shot of the area see http://www.hurstcastle.co.uk
The best thing about this area is that it's quiet, despite how beautiful it is. I think the walk puts a lot of people off, it's also largely shingle so not many 'beach goers' would want to bathe there. It does seem to be very popular with fisherfolk and we passed several dotted along the spit merrily fishing away, some camped out ready for the night. I took some photos along the way, it was a lovely day but very bright so I decided to shot in black and white, to add a bit of drama.