I'd consider doing a tapas crawl. Choose a classic street like Cava Baja. If a 'wild street' is too daunting you could go to San Miquel Market which is kind of touristy but has lots of tapas stands, drink stands etc in one space and is festive and super easy to manage. It is in an ancient covered market building and is very picturesque. The food is better and a lot cheaper doing it on your own but the Market is likely to impress a 14 year old and be very very easy to negotiate. And you can in addition to tapas have pallela and lots of fancy desserts. It is a place where you walk around and sample food not a place to sit at tables and enjoy dinner -- it is a tapas crawl but in one space. (Bars in Spain are like cafes/coffee shops in the US not adults only boozy places at least fairly early in the evening) AFter we stumbled on the San Miquel Mercado and had a bite to eat we went to a nearby shop on the same square and tried the churro dipped in hot chocolate. Don't order more than one of these -- they are incredibly sweet and even this sweet tooth couldn't come close to finishing one. But it is a think to try at least once.
A restaurant we went to that had amazing creative tapas (one was wrapped in rice paper printed with the front page of a newspaper for example) that were also super tasty was not far from Plaza Mayor was d'Fabula. For tapas it is best to go for lunch as they really don't want to give you the tapas menu at dinner (it is not a bar but restaurant) the tapas were very cool. It is at Plaza Conde de Barajas, 3, 28022 Madrid, Spain
A place that a lot of people miss but that is super easy to visit and pretty amazing was the Basilica of San Francisco el Grande https://janettravels.wordpress.com/2013/10/23/easter-egg-in-madrid-basilica-san-francisco-el-grande/ No crowds and very cool.