You could check out your local theatre for shows, one local to us does horrible science live shows, it looks great.
You could also book one day courses for surfing, windsurfing, kite surfing 'm trying to think of other sports that don't involve getting wet but can't just now.
Go karting or underage driving, you can start at 16 round here as there is a place that does lessons on private land.
Beach clean up, this usually takes place at the end of the season, it's a day out of sorts.
Indoor snowboarding, you can do a one day beginners course.
Science museums, not just London there are others.
Exhibitions e.g ideal home show, motor show you can often get discounted tickets for these.
If you're a bit skint one day just pack some watercolours and get the family painting at a local beauty spot.
Music festival, kid friendly ones include bestival and larmer tree
Can you start by looking at your local tourist info office and local publications, there should be plenty of adverts.
I love this idea, think it's way better than tons of toys.