Barcelona Tips:

Barcelona is incredibly walkable, so be sure to pack your appropriate shoes
Catalan is the main language here, not Spanish, so don't be surprised when you see and hear it being used. Basically everyone speaks both Catalan and Spanish but there is a lot of tension between Catalonia and the rest of Spain
There is a super convenient shuttle to and from the airport called the A2 I would highly recommend

Abirradero: A brewery popular with locals, sit outside and enjoy a flight (I also highly recommend their cheese plate obviously)
Casa Batllo: My favorite of the Gaudi works, check out this gorgeous house
Barcelona Beer Co: Definitely catering to American tourists, but they make delicious beer so it is worth your time
Barceloneta: Time to hit the beach! Marvel at the yachts in the harbor, wade into the sea, then grab a drink at Arenal Bar right on the sand. Preferably cava sangria [yes you read that right. sangria made with champagne]
El Born neighborhood: the more "hipster" neighborhood full of bars and restaurants
Eixample neighborhood: home to some of the Gaudi works and a slew of restaurants
Palau de la Musica: See a show in this gorgeous music hall, tickets can actually be reasonably priced

La Sagrada Familia: The infamous church that may never be finished. It's exterior facade is one of the most intriguing things I've ever seen
Park Guell: The classic Gaudi park in the north of the city. They limit the number of people that can enter per hour, so book your tickets ahead of time and try to choose an off-peak time
Cathedral of Barcelona: Absolutely stunning
La Boqueria: Food market right off Las Ramblas

Take a peek at the Arc de Triomf. Pro Tip: Go early before there are too many people passing through
Maestro Brewery: Centrally located and solid beers
Casa Mila: The least exciting of the Gaudi works, but still much more interesting than your average building
Garage Beer Co: Average brewery with some interesting collaboration beers
Guell Palace: Worth a quick look while you're meandering the city

Get into the Pyrenees Mountains!
- I went with Explore Cataluyna and we went to the medieval village of Besalu, then took the curviest road up a mountain to the tiny town of Rupit, then ventured to Tavertet after stopping on the mountain side to gaze at the view

Skip:

Las Ramblas: Sure you might be thinking "but I have to see Las Ramblas while in Barcelona!" Okay fine, but make it brief. This famous street is extremely far from the "real" Barcelona. Do not eat or drink anything while near this area unless you just like wasting money
Montjuic: This castle and park is pretty overrated and the funicular ride up to it is a short but expensive ride
Picasso Museum: If you're a big art fan, go for it. If you're an average art fan like I am, I found the museum less than worth the relatively high price and extremely long line to enter