At this age (or indeed at most ages!) reading Shakespeare's plays drily on the page will probably not be very inspiring as a starting point - they were written to be performed and watched after all. Did you catch the BBC production of Hamlet last Christmas with David Tennant - it was stunning. If you live close enough for a trip to Stratford-on-Avon, seeing Shakespeare live with brilliant actors & staging really brings the text to life: you don't have to understand every nuance of the language (which to be honest most of us don't) but can be carried along by the action, with the beauty of the language seeping in almost subconsciously. There are some children's books (Horrible Shakespeare? Top Ten Shakespeare or similar) which help to give enough of the essence of the plot to be comprehensible while picking out some of the poetic "highlights" of the text, which could be useful before watching a production. Look out next summer for one of the touring productions which often pop up in local parks/National Trust gardens (weather permitting!) - we saw an excellent Romeo & Juliet locally.
Also many children enjoy the Shakespearean insults, as well as discovering how many well-known phrases are quotations from one or other of his plays. See http://www.rsc.org.uk/education/primary/
for some other possible ideas to explore - and definitely make time for a visit to Stratford!