My wife and I recently took our two daughters (ages 4 and 1 at the time) to Europe. We had a great time and there is plenty to do that your child will enjoy too. London was by far the best city for kids in my opinion. Despite what I have heard elsewhere about kids not being welcome in English pubs, etc. we found everyone to be very accomodating and a ton of things that interested our older one. The British Museum was also a hit. We also drove up to Warwick Castle. Its interesting from an historical perspective, but (owned by Madame Tussauds) is a little manufactured for my tastes.

Paris was fun but restaurants were tough with the kids. We did a lot of cafes and street vendors, plus we rented apartment an aparmtnet, allowing us to cook on occaision.

I haven't been there with my kids, but Madrid is pretty child friendly IIRC. The Retiro is great on a Sunday.

Keep in mind though that all European restaurants will have smoke - lots and lots of smoke. Its not as big an issue over there as it is here. Also, you will end up taking twice as long as you think you need with a little one. Getting through train stations, buses, exhibits, parks, is a much slower process. We had to seriously revise our list of things to do once reality set in over there.

All that said, it was definitely worth going. We had a great time and so did our daughters. I am sure you will have a great time too. Good luck!