If you're doing it in your house, you could print pictures of characters from the story - Cheshire Cat, White Rabbit, etc. and hide them in different rooms, with the clue to the next one written on the back. Something like -
Head to the kitchen
In a spot you might wait.
The one you'll find here
Doesn't want to be late!
(leads to the White Rabbit, in/near the microwave)
My friend in the playroom
May think that he's clever.
But when Alice is lost,
He's no help whatsoever!
(leads to the caterpillar)
and so on.
You could hide real objects too, if you have enough of them - like a deck of cards, a pocket watch, etc.