3.5 day Itinerary Barcelona

Max out your time by adopting the cultural habits of Spaniards and learn to eat tapas early evening, dinner after 10 p.m. and then stay out after dinner. Seriously, tourists often miss out on the ability to enjoy an important part of the Spanish culture by allowing their eating habits to remain on the time table in the USA.
Sure you could do all three in one day if you simply desire to say "I have been there." Even though you have just a few days for this journey I recommend a focus on quality vs quantity. La Sagrada should be a minimum three hour visit and be dure to go up at least one of the towers. This is an truly unique place meant to be absorbed. Then make a choice between the two Casa's and enjoy the visit. You don't need to see all his most natable works in order to gain an appreciation of his genius. Btw: i would skip Parc Guell, especially since day light will be precious at this time of year.
I highly recommend going to an evening concert at the Palau de academy of music. Check it out on the web. A fascinating place and a concert will place you among the locales to provide an appreciation from their perspective. Dont get concerned about what type if music is being offered nor the seat selection. You will understand once you attend.
Party like the locals......... And you are in your 20's........ Sorry, I am passed the age limit to be able to privide guidance on this issue (darn it).

One thing I would suggest is to book your tours online. This will save a lot of waiting time. Also the metro is easy. Buy a 10 pack and you can use it between the two of you. And the taxis are pretty reasonable! We went from Train station Franca to the Sagrada for about 7 Euros. And just like anywhere, watch out for pickpockets. Just be aware of your surroundings. We have been living in Spain for 3 years and have not had any problems. But have heard of many people getting pick pocketed, even Spaniards.
And if you are staying in El Born. try to see the church Santa Maria de Mar!

3 easy days to see the best sights of Barcelona...

Day 1 - Barcelona vistas
From Plaza Espana head up Montjuic to the Olympic Ring and perhaps visit the Joan Miro Foundation.
After lunch at one of the great authentic tapas bars in Eixample make your way to Parc Guell for another great view of the city.

Day 2 - Historic Barcelona
Start at Plaza Catalunya and walk down the Ramblas to the Port visiting the Boqueria Markets on the way. Explore the nearby Gothic Quarter dropping into the Picasso Museum. If time allows visit Palau de la Musica.

Day 3 - Gaudi Barcelona
Start at Plaza Catalunya and walk up Passeig Gracia for Casa Batllo and La Pedrera.
Take the Metro across town for Sagrada Familia. If time allows visit Hospital Sant Pau.

Marbleskies give the same basic recommendation I would make. I will add that you should get your tickets to Sagrada Familia on line before you go to Barcelona. You will avoid what is usually a very long long line to get in. Walk up to the front of the long line. You will see a much shorter line to the right with signage indicating "Ticket Holders" or some such. Go in, sit down and enjoy the amazing edifice that is still under construction.

In January with limited daylight, it might be a stretch to see all three Gaudi sites in one day. And it might cause Gaudi burnout. Casas Batllo and Mila are very close to each other and at this time of year should have very short lines. Both are easily seen in a day. I do recommend the audio tours but the video tour (more expensive) aren't really worth it. Sagrada Familia can be busy any time of year and I do recommend getting tickets online in advance. Especially if you want to go up a tower (a nice thing but by no means a requirement). If the weather is nice, Parc Guell might be worth the trek out but not if the weather is poor.

Fat Bike Tours: saw Sagrada Fam (didn't go inside, tho...) Olympic site, the beach, Roman walls, arc de triumph, and other things. fun riding the bike around town. took about 4 hours. Quite a few young people on the tour, so you might enjoy that, too.

I suggest you see both Casa Mila and Casa Batllo from the outside, but tour only one (my preference would be Batllo). They are very similar, and the tours are not cheap.

For a true foodie experience, I would really try to go to Tickets. It's too late now to get a reservation, but if you're up for going to the bar and waiting for a table to open, it's totally worth it.

Also, definitely go to Tapas 24 and Cafe de l'Academia (great Catalan cuisine).