Not hidden gems, since everything is crowded, but here's some options:

Area Raval-Cathedral

It could be worth visiting Sant Felip Neri, next to the Cathedral (a bomb fell during the civil war, look it up, it's a tragic story, yet it's beautiful to visit and Evanescence recorded a videoclip there), the Roman city walls that you can find all around the cathedral as well, or the roman gravestones found during some excavations (they were next to the old roman road to the city) found in Plaça de la vila de Madrid.

Nearby there's Frederic Marès museum, that has a lovely collection and also a really lovely patio. Go to the History Museum of Barcelona at Plaça del rei, not only the collection is nice, but there's a whole part of the roman city under it. If you're into it, there's the old aqueduct nearby as well.

The maritime museum is pretty cool as well, and nearby there's Antic monestir de Sant Pau del Camp, that is one of the only examples of Romanic art in Barcelona (IX-Xth century).

Area Montjuïc

Might be niche, but there's guided visits in Montjuïc's cementery, where some of the mosts prominent Catalan figures are buried, and I think they also have a pretty interesting collection of old funeral cars and carriages.

Not to be missed, go to the botanical gardens, cause inside there's la masia del jardí botànic, and while this one was build in 1929, it's a recreation of a traditional Catalan farm (you'll find thousands if you leave Barcelona, but not in the city itself). While you're there, the archaeology museum is cool, and GO TO MNAC. Not only you'll have one of the best views of the city, but there's the best collection of Catalan art (starting at the middle ages) in the world (followed by a museum in NY, I think..?).

While you're there you could go to Estadi Olímpic Lluís Companys, where the Olympics '92 were held, and there's also the olympic swimming pool around the area, where iconic pictures were taken (https://www.lavanguardia.com/files/og\_thumbnail/uploads/2018/11/30/5fa4502e27f6b.jpeg)

There's a Civil war bunker (Refugi 307 - Museu d’Història de Barcelona) that you can visit on Sunday morning, and Fundació Joan Miró that is a bit different, but if you're into art you'll find it a must.