I was just there 2 weeks ago! We had the best time. I honestly think winter is such a good time to go to Barcelona as long as you don't need to go to the beach, it's less crowded and the weather is still very pleasant. It's a great city to just wander around in.
Here is a (not comprehensive but very long nevertheless) list of things we enjoyed.
The Picasso museum was great. They have a lot of his earlier stuff, and it was cool to see how his style evolved. There's also a series of 60 (I think) different paintings inspired by a single Velazquez painting that are really cool.
We did all the big Gaudi buildings (Casa Mila/La Pedrera, Casa Battlo, the Sagrada Familia of course, and Parc Guell) while we were there, because we love looking at cool architecture. Any one of them would be worth a visit if you like that sort of thing. I think the Sagrada Familia is obviously the most impressive, Casa Mila is great if you want to learn about Gaudi. They all come with pretty comprehensive audio tour guides.
If you are at all into music, you might want to try to go to a concert at the Palau de Musica Catalana. Even if you're not, you can take a tour in the mornings, the building is absolutely gorgeous.: https://www.palaumusica.cat/en.....BpyzCh1JJA
Tickets for almost everything are cheaper online than in person, and you don't have to wait in line if you just buy them on your phone.
Definitely go to this bakery/sweet shop by the cathedral: https://www.pastisserialacolmena.com/en/
This place has really amazing, fresh seafood (see picture below): https://www.instagram.com/kioskouniversal/ It is in the Mercado de la Boqueria, the big market in the Gothic Quarter, which is fun but can be a bit too touristy sometimes. Still, it's really fun to walk around the market, buy some fancy ham and fruits, etc.
Super nice pastry shop with delicious croissants: https://www.hofmann-bcn.com/en/patisserie
If you're into gin, there are amazing gin bars in Barcelona. We liked this one a lot: http://www.cactusbar.cat
And there are of course millions of places to get tapas and pinxos in the evening. Honestly you could just walk down some of the streets in El Born or the Gothic Quarter and walk into one that looks busy and it'll probably be great.
This tapas place is super cute (but tiny, so getting a table might be difficult), and the food is different than most of the others: https://www.tripadvisor.com/Re....._Catalonia.
