Magnetic tie downs work quite well to a point. They are fine if you want the puppet to just kind of shuffle along, not really takeing its feet of the ground.

I have always filled in the tie down holes with clay which is colour matched to the animation surface. I nearly always do this even if the holes are going to be removed later in post.You can use any photo/paint programe to achieve this as well as rig removal. As with anything in this field, it can be fiddley.

Thank you all, will have a go at all of the suggestions and see what works best for me. I have found someone who makes tudor dolls houses, and is interested in using them in an animation as part of the set. He wont want them drilled into so I might need to watch marc's DVD again to learn how to make a rig.

Heh, I remember bugging Nick Hilligoss with this question a while back.
There are a few ways to hide them, depending on the camera angle you can sometimes just leave them bare. You can also fill them in with a blob of clay with a similar colour to the floor. You can also comp them out, or with tiled and plank floors, you can replace the tile that has the hole in it with a solid one when you need it. With Grassy and muddy floors you can usually get away with leaving them exposed.

Magnets.. uhh...
They need to be strong. Really strong. Like, "If I slip, this will shatter my fingers" strong.
You also need to make sure the magnets are under the set rather than inside the puppet's foot, because if they're inside the foot, you won't be able to have the foot near to the ground but not touching it, you also won't be able to have the foot having only part of it in contact with the ground. You need these things for walks.

It depends on your budget.

Tie-downs are a lot cheaper than using earth magnets.  A couple wing nuts and metal rods will cost you about $5.00-$6.00, whereas earth magnets can cost you an upwards of $40.00-$70.00 a piece. 

Both systems work absolutely fine if you know what you're doing.  I've never experienced any problems with my magnets during animation.  However, as anileator said, you will end up pinching yourself a few times.  These magnets aren't friendly to careless fingers.  Also, if you have uneven terrain it's a bit tough to use a magnet. 

Since you said your friend doesn't want you to drill into their doll house, I would avoid using their dollhouse altogether; unless, of course, for a background shot.  The rooms in a dollhouse are usually very narrow and deep.   It would be difficult to animate in such a space.