My kid was (and still is) all about the BMX riding.
His first 'real' bikes were a 16" Haro 116 BMX 'park' bike and a Redline 20" BMX racing Proline 'Mini' (you might want to go even smaller to a 'micro-mini'. Sadly, as I'd love a 6-pack, I just sold off both of these this summer, as he moved up to an 18" BMX and 24" MTBs.
If you're near Bedford, I'd highly encourage you to take him for a little road trip to the Billerica or Wakefield BMX tracks, as well as the Russell Mills pumptrack. Great places for kids to start riding dirt, and you can ride there any time you want as long as there's not a race going on (it's fun to check out the races too - both tracks have websites with schedules; lots of young kids go racing). The fields at Great Brook in Carlisle are also a good place for little ones, plus they've got the ice cream stand, etc.
If you're a weight weenie, you can go on the Families and Kids sub-forum on MTBR.com, where guys that make their kids go out in public wearing spandex will give you all the info you need (and then some) on how to spend shitloads of money and time saving some grams, but from what I found, the fact that most kids' bikes are proportionately very 'heavy' has never kept my kid from ripping on them.
Slapheadmofo Leisure Team
Sunday River Bike Park