How old are they and you, if I can ask?
I babysit my lil' cousin who's 4 now and I noticed it's always better to get out the House.
Get a Ball and take them to a park for football (or soccer if you insist on calling it that

), take some food / Drink and get them to take their Bikes down when they visit. It's a classic good day out or afternoon and best of all won't cost a penny and will knacker them out too

.
Maybe see what events are on locally? I took my little Cousin to Brighton Modelworld with me and some friends. It was literally a Model Convention with boats, replica steam trains, characters etc. They had the Robots from Robot Wars out on the day too with actual Blades and Flamethrowers.. not sure who enjoyed it more, me or him lol.
If you can afford it, or your Parents are ok to fund it.. The Cinema never fails!
EDIT: If you have to stay in, DVD (introduce them to TLK lol) and I like to break out my old Games and Toys from the Loft for my Cousin too. He plays Super Mario on the old Snes

quite a bit.