Hey Geoff, Kamakura in Kanagawa prefecture should be your answer! Apparently it's really beautiful. And one of the contributors, Larry Knipfing, did a little photo story on it as well. Looks pretty great!
The stretch of beach between Kamakura and Zushi is very popular in the summer. You'll see loads of people having barbecues and picnics there, or going surfing, and there are sometimes events held on the beach itself (music etc.). Personally I don't think it's that great, however. There tends to be quite a lot of rubbish left on the sand, and the beach itself isn't that pretty. It's one of the most accessible beaches from Tokyo, though, so if all you're looking for is somewhere to lie down in the sunshine and perhaps dip your toes in the sea, it's very easy to get to in just over an hour.
What's important to remember when seeking sun and sand around Tokyo is to either go during the week (NOT a public holiday), or to take public transport. Several years ago on a Sunday whim our family decided to "pop over to Chiba" via the Aqualine, by car. We got about half way before we hit the traffic. In the end it took 4 frustrating hours to find a beach and another 3 hours to get home again late that night. In the week, probably we could have done the same trip in an hour and a bit.
So public transport to where? Well, the most accessible locations from central Tokyo are probably going to be Hayama in Kanagawa-ken, which is about an hour and a half on the very frequent JR Yokosuka Line, and slightly further west to Enoshima on the also very frequent Odakyu Line (Romance Car), and which takes about an hour twenty minutes.
Reachable by local train (JR Tokaido Line) or special rapid express (Superview Odoriko) from Tokyo in an hour or so, town beach of Atami at Shizuoka Prefecture is a good spot to feel the real Japanese summer (and it's madness). We went there to see hanabi in August.