For sight-seeing, probably the biggest and most important thing is La Sagrada Familia.
You have to go inside. I didn’t the first time I went to Barcelona. The second time I went, I wish I would have gone initially. We only spent 30-45 minutes there, so it’s not an all day thing. If you can schedule/arrange it for a sunny day, it’s highly recommended, for obvious reasons.
You can pre-buy tickets from their website (https://sagradafamilia.org/en/tickets-individuals) to go inside. The inside is as, or more, dramatic than the outside!
There are also a couple of other Gaudi architecture pieces in the city if you want to see them. I know at least two are on Passeig de Gracia (that’s the name of the street) One is called Casa Batllo, the other is called Casa Mila.This is Casa Batilo.
EATS!
Now, onto the fun part, food. My absolute must visit spot is a cheesecake place. You may or may not know Basque cheesecake is a pretty big thing. While this isn’t Basque Country (other side of the country, San Sebastian actually) This place does some seriously amazing and cheap cheesecakes. The place is called Jon Cake. They also just opened a new space, which adds a wine bar. (https://www.joncake.es/en)
There is/will be a line, but it moves quick and is so worth it. The OG spot on Carrer dels Assaonadors is probably the best and closest to where you’ll be wandering. Right in the Born neighborhood. It’s the one closest to the water. Easy enough to find if ya search for it.
We also found a bar we loved, You can sit inside the awesome bar or you can sit outside and enjoy a drink or two. The spot is called “La Mariposa Negra”. https://mariposanegrabar.com/ We were in Barcelona for 3 nights and went here for two of them. We liked sitting at the bar watching the bartenders create these concoctions.
Two great spots for lunch snacks/tapas: One is a hole in the wall about 3/4 mile to a mile away from the Gothic Quarter. The place was called La Cova Fumada. https://www.lacovafumada.com/ (Address: C/ del Baluard, 56, 08003 Barcelona, Spain) The Calamari, the bread with tomato sauce (forget the name), chorizo, mussels…. Not many tourists here. But we thoroughly enjoyed it.
The other spot is a famous spot, which can get busy called El Xampanyet. I’d go right when they open to ensure you’re not waiting too long. Get a glass of their local Cava while you’re enjoying some tapas. https://www.tripadvisor.com/Restaurant_Review-g187497-d697571-Reviews-El_Xampanyet-Barcelona_Catalonia.html
If y’all get tired of eating all this amazing food and want something familiar. We went to a phenomenal pizza joint called Parking Pizza. (Address Pg. de St. Joan, 56, 08009 Barcelona, Spain) http://www.parkingpizza.com/ There are a few of them across the city. So there may be one closer to you.
We also had dinner at a place called Benzina, which was a bit more of an italian style dinner. It was packed, so reservations are suggested. I went there both times I went to Barcelona and had a great time. https://en.benzina.es/
I think that’s all I have to guide you on food stuff. We’re obviously food snobs, but all of this is extremely reasonable, if not super cheap.
For Transportation, there’s a bus that runs from the airport to downtown Barcelona and back that is SUPER easy and cheap. It’s 5.9 Euros each/way. And makes life very easy. With 4 of you, you may get a taxi, but that’s up to you. The bus site is found here:https://aerobusbarcelona.es/?lang=en It’s 24/7. You can buy tickets early and it’s just walk on walk off. Super easy and cheap. It’s about a 15-20 min bus ride to the Gothic Quarter.
Also, their subway is super easy to navigate. So feel free to use that for when you don’t feel like walking a ton, though we walked everywhere!