My kids (and I) enjoy "robot" kits.
Maplin do a couple of kits for light seeking robots. Basically they
have a left and right circuit which is an LDR controlling a small
motor. No wheels - the spindle acts directly on the surface. PCB is
supplied and you get to do the soldering. Much more learning if it
doesn't work first time. They're fun to build and then fun to play
with (darkened room, torch, smooth floor).
Rapid are big in education and do quite a few really good kits which
are suitable for 13 year olds and not too expensive. The best we've
had was the "brainibot" which is a programmable bot with light, touch
and sound sensors. They do three versions, the most complex of which
is programmable by hand or from a PC using a command language - about
£15 from memory and you (sorry they) get the fun of doing the
electronic assembly, mechanical build from raw components and setup as
well as then developing your own programs for different movement
strategies. I recommend it most highly.

Don't worry about the lead free rules by the way. It's (going to be)
banned for maufacture but not for rework so the solder will still be
available (manufacture doesn't usually use solder on a reel anyway).
The old common sense still applies, don't breath the fumes, don't eat
or drink while working and wash hands afterwards.

Cheers,
Calvin