your "Anything that I missed?" question put indeed a smile on my face.... you're not even scratching the surface, my dear. You could spend a month here and with the possibilities of the city plus the escapades to other wonders in the region you'd be doing different stuff every day and still you'd probably be missing "something". Fun facts: with all the magnificent possibilities around the world, full of gems everywhere, 42% of the first visitors to Barcelona do return a second time, 24% a third, 14% a fourth or more. That should say something. [Source: stats (2015) at the Barcelona Tourism Bureau, barcelonaturisme.com]. So, the first rule for visitors: you'll be missing a lot, period. Do a bit of research (you have hundreds of sources online and offline about Barcelona) and then carefully pick your venues so you get the most out of your time here.
I share your view of not planning your days with too many things, I also favour time to "soak" in the local flavour, for me, it's the best way to get to know a place.
A few considerations:
- IMHO La Sagrada Família is far more impressive inside
- You do need reservations for ALL popular sites in the city, especially in Summer, or you'll be queuing for ages under a scorching sun. Do pre-book them online. And yes, Park Güell is also a popular site. As a general rule of thumb, when in Barcelona, thinking about just "turning up" is generally a bad idea if you really intend to visit the site.
- Tramvia Blau is for now out of commission. Maintenance works are being carried out.
- I would consider a visit to a very small museum at the Casa dels Entremesos, located in the Old City, very close to the Palau de la Música Catalana -which is also open for visits, but again, you need to pre-book. You kid will be able to see up and close the bestiary of our heritage giants and big heads that are part of the traditional festivals in the city. This is a short video of Casa dels Entremesos -which, btw, has free entrance- and this is their website.
....ALL THINGS TRANSPORTATION
On Sunday afternoon, as a special treat for your kid "fan of all things transportation", I'd consider making a short escapade to Vilanova i la Geltrú, a town 40km south of Barcelona reachable by train in under an hour, to see the Catalonia Railway Museum -which, incidentally is just next door from the station. Actually, if you like some time down at the beach, Vilanova i la Geltrú is also a great option as the beaches are a tad less busy than the ones in Barcelona.
Other transport-related ideas...
- a ride in the cable car (Aeri del Port) over the harbour in Barcelona,
- a visit to Montserrat, where he'll be taking up to four means of transportation: bus or metro to Plaça Espanya in Barcelona, then train to either Monistrol de Montserrat or Olesa de Montserrat -depending which means you use to ascend to the monastery-, then either the cable car or the rack train to the monastery.... and you can then switch these last two on your way down when you return.
And a bunch of other kid-related activities in this old post of mine at TA.
Enjoy!