24"
We bought our 9yo daughter a 24", and glad we did. She is now 10 and tallish for her age (95th percentile, don't know were she got that). I was looking at $300-500 bikes, and my wife said no way, she will outgrow it too fast. She previously had a $400 Specialized 7sp 20" Hot Rocks that I found used for $100.
We tried her on some small framed larger wheeled bikes. I simply didn't like the fit, mainly she was stretched out too far, and the bikes were heavier and hard for her to handle.
So we bought her a 24" GMC road bike from Amazon for about $150. Are the components great? Nope, but serviceable for a couple years. This size 24" (At least 4 on the market, see metric size) will also take skinnier road tires, but comes with almost perfect mid width tires for our local gravel rail trail. It's not unusual for her to ride 10-15 mile rides with me, but most are 4-6.
Accept she didn't like the road handlebars, so swapped them for a simple alloy riser bar, and bought brake levers (the stock shifters are straight bar type anyway). A regret is not splurging $35 for combined trigger shifter / brake levers. We have about $175 in the bike as it sits in the garage.
My advise is to get the 24" if you can, or make sure she fits on a small framed larger wheeled bike properly. I also regret selling my wife's xtra small framed Trek 7.3fx 700c bike we special ordered. She could physically ride it when we purchased the 24", and would have actually fit in 1-2 more years.
I attached a pic of her stopped off a rail trail earlier this spring very close to her 10th birthday. Don't notice the highly customized Townie beside it, we have more in mods than the bike cost =}~