I let my 3 year old choose between a Trek Mystic 12 and a Haro Z 12 and surprisingly she chose the Haro. I thought for sure she'd have gone with the more girly of the two. The Trek is a nice little bike and sounds like what you're looking for.
The Haro...
I like the Haro's seat (it's bigger) and B&P cycle was able to fit a chainguard on it for me. It comes with the handlebar and crossbar pads (not pictured) just like a real bmx. (and training wheels) : )