making a bot follow an invisible track

I want to make vehicles crawl around a LEGO town following a path I
define -- but in some invisible way, so the onlookers can't see how it
works.  What are my options?  Here are some I've thought of, but perhaps
you can think of something better:

1. Put strong magnets under the road, every few cm, maybe closer
together on the curves.  Magnetic sensors of some sort (maybe just reed
switches would do?) in the car would use this to steer, much like a
traditional optical line-follower.  Problems: the road can be almost a
cm thick itself, which would necessitate the use of strong (and
therefore expensive) magnets.

2. Put cheap iron bars or balls (or whatever) under the road, and a
strong magnet on a swivel in the car.  The magnet should point at the
nearest iron, and we can detect that (maybe by bouncing an LED off it)
and use it to steer.  I'm not sure if this would work reliably.

3. Er... getting short on ideas here, but if we could embed some sort of
navigation beacons in the town layout, then in principle you could make
the cars "programmable" by manually pushing them once around the path
you want them to follow, and they should be able to repeat that path
again and again.  But I'm not sure what sort of navigation beacons would
be appropriate -- remember, neither the car nor the town is supposed to
have any visible gadgetry; it's supposed to look like the minifigs are
just driving their cars.

4. Really scraping the barrel, could we do some sort of optical
line-follower but not in the visible light range?  Something we could
use to paint a line on the road that would be invisible to humans, but
visible to the car's sensors?

Any insight on the above ideas, or new ideas I haven't considered?

Many thanks,
- Joe