Later on, I felt limited by how they were designed, and found that 'Free Radio Berkeley' sold kits to build pirate radio stations, which I thought was the coolest thing I'd ever found, so I ordered some kits from them to work on. It turned out that the kits were missing quite a few parts (which weren't available through Radio Shack), so I had to search & find mail-order electronics suppliers to order the missing parts from. Another thing that was 'wrong' with these kits, which I had to find a solution for, was that they only included pictorial schematics- no use of standard electronic schematics like you'd find everywhere else. So I had to draw my own schematics based on what was present on the circuit boards. This eventually helped me in the long run, as I was able to bring the transmitter + the schematics I drew up to job interviews, & I landed my first electronics repair job based on my work on the transmitter.
EDIT: Another thing you might look into that I found educational/fun is mods for CB radios. A good CB shop can sell you a CB Radio & parts which allow you to make some changes & add extra functions by making simple alterations to the circuit boards. I added more wattage, a frequency slider, extra channels above & below the standard 40, & sideband to a Cobra 148GTL back in the day. There was a small community of people on the radio where I grew up, & I would stay up late at night talking with them on my fancy radio. Later I got a linear amplifier, but was always afraid to use it since they're illegal- so I got rid of that to play it safe.
http://www.kohls.com/product/prd-1604010/elenco-200-in-1-ele...
They still sell the old RS stuff on Ebay. I guess those Arduino boards are nice and all, but kids like to create things sometimes, not just play with pre-made stuff. I loved to tinker with things when I was a kid (and not just take alarm clock guts out and stick them in a different case) so those kinds of kits really kept up my interest.
As time goes on and as technology progresses, the minimum parts or components used while "making something oneself" become more complex. For example, there would have been a time when making your own capacitor using glass jars and chemicals, or making your own light bulb using a vacuum pump, would have been the equivalent of making your own remote-controlled car today. Every generation builds on the advancements of the previous generations. Failing to do so may doom one to focus only on the advancements of generations past. At the same time, I definitely understand the nostalgia of imagining your modern child experiencing those same things you did when you were younger. The problem is that the world changes too fast for this approach to really be advisable.
Later we bought her a "Arduinos Sparkfun Professional Inventor's Kit", but she didn't play with it too much. (This is more expensive (x2 or x3) that buying each part separately but it's a nice starting kit and has many initial projects. (Buy more LEDs in the local store, they are cheap and nice.))
For more ideas, I remember a very interesting page: The Sylvia's Super-Awesome Maker Show! : http://sylviashow.com/
It's basically pens filled with some kind of metallic ink that conducts electricity. It comes with "blocks" you place on a paper sheet. You use the pens to connect the blocks.