For the price I ended up getting my daughter a Schwinn at, hold your breath, Target. It is a steel frame (so heavier than the aluminum ones out there). I was really down to this or a Fuji alum. for about $215. The price finished the deal for me and my daughter is 7 and very tall for her age so I didn't see the expense. The Schwinn has a Tourney rear derailler (as do most of the others), rack mount screws, water bottle screws, 21 gears, SRAM shift, promax brakes, threaded regular headset ... all for $108 on sale. It just seemed to add up to a good value for the money. I also want her to handle some nice rides (for my sake) ... but I honestly don't mind if the steel wt. slows her down a bit. She really zips along! Cautious mother here. It feels pretty solid and does have parts that can be worked on should the need arise. It really isn't all that heavy ... I've thrown it in the van a couple times already.
the Trek & Fisher looked about the same to me (not a big surprise).
Raleigh & Giant also offer nice 24" bikes as does probably all the major makers.
Good Luck!