I took my 5 year old to Barcelona in October half term and was pleasantly surprised how child friendly this bustling city is.
The award-winning zoo was quiet this time of year so very few queues to get into the sea-lion and dolphin shows. It was also warm enough to picnic in t-shirts in the many park areas. We took a hop-on-hop-off 2 day ticket as my little one wasn't up for all the walking. The ticket also gave discounts off many attractions and restaurants, including the zoo!
We found the metro to be very handy, good value and easy to navigate too. If you buy a multi trip ticket it can save you a fortune.
An area we found to be ultra cool was 'El Born' - trendy tapas bars, shops, small hotels and great Spanish architecture really close to the main Gothic Quarter but nowhere near as busy.
Definitely worth a return visit, without children next time, so we can enjoy the late night Spanish lifestyle!
TIP - Make the effort to visit Gaudi's Parc Guell, north of the city, it has amazing views over the whole of Barcelona and out to sea.