I want to start our visit to Madrid with a fun tour of sorts. Any suggestions?
I suggest Madride walking tours as they're led by lovely, knowledgeable and fun people! also they can give you great recommendations for your stay in Madrid. I did one and it was great- fun and informative, and not too long.
they start from the Puerta del Sol in the centre, by the Bear statue. Look out for the red T shirts/Umbrellas! Their logo is a bear.
Mentioned in this answer:
You can have a Segway tour with a professional guide Madsegs in madrid just in front of the Mercado de San Miguel and Plaza Mayor. You can rent this tour for 45 minutes or 1 hour. Its kind of cheap for such an amusing tour and the guide will take through many touristic places and will give you a brief info about the places.
Good luck and enjoy