Anything by Gaudi!  He has several well known places in town, even though they aren't off the beaten path, there is nothing like them anywhere else in the world.

Parc Güell; Basílica de la Sagrada Família, Casa Batlló, Catalonia La Pedrera are the absolute must sees....

I would recommend Parc Güell! You have to do a little walking/hiking up stairs, but the view is fabulous.  

It originated as a real estate venture gone wrong by Guadi and one of his buddies, Guell. They were designing a nice neighborhood for wealthier people to live in. At the time, it was just outside of Barcelona in the foothills of the Sierra de Collserola, which provided great views of the city and ocean. The problem was, none of the upper class wanted to move that far away from the city center. So, Guell made it a park and named it after himself.  

Today, entrance to the park is free. If you want to visit the Gaudi House Muesem (in which Gaudi lived, not designed), there's a small fee. It's a fun place for kids to run around and everyone to get some fresh air. The park is not too far from the city, but definitely not waking distance. I'd suggest a cab or the rail system.

Hi Allie

In my book #BCN - by locals I over the off the beaten track architecture jewels. To name four of them that I think to be worth visiting...

1. Pritzker award wining architect Toyo Ito's Hotel Porta Fira

2. The Disseny Hub Barcelona (DHUB) at Plaça de les Glòries Catalanes, a beautiful addition to this changing part of the city

3. A modern classic by Mies van der Rohe built for the World Exposition 1928 close to the Plaza España: Mies van der Rohe Pavilion

4. Parc Güell

Catalonia Plaza Catalunya, Andante Hotel

Enjoy Barcelona! Best, Jahn

Barcelona is famous of Gaudi works. Sagrada Família is one of them.

So besides that you should  definitely visit:

Casa Batlló

La Pedrera

Güell Palace

Parc Güell

All of them were made by Gaudi.

Of course walking root through Barri Gotic will be awesome.

Hi Allie. Barcelona is full of great architecture. If you don't have a place to stay you could actually stay in Barrio Gotico by looking on http://www.loquo.com/en/barcelona/ for a place to stay. A walk up Passeig de Gràcia, Barcelona you'll be able to see a few interesting places with great architecture. The architect of La Sagrada Familia - Gaude has a few great places to see around Barcelona. Make sure to stop by Parc Güell, it's simply amazing. I'd also recommend, though I never did it but everyone said it was worth the effort, to check out the Dalí Theatre-Museum which is a little outside of Barcelona. Hope you have fun.

if you can get out of town in a car, La Colònia Güell is great. Moderniste architecture and you don't have to share it!

Hey Allie, those are some great places to see iconic architecture in Barcelona. A place that's a little off the beaten path that I really liked is the Plaça de la Virreina in the Gràcia neighborhood. There's a nice church and a plaza with a bunch of cafes. To the left of the cathedral, there is (or there was 4 years ago) a piadina shop called La Piadina which I loved. Piadinas are like Italian quesadillas. They're cheap and awesome.

I'd also recommend seeing the castellers if you can. The castellers are organized groups of people that create human towers (castles). So it's not exactly architecture...but it's pretty close. 

http://www.castellersdelaviladegracia.org/ - that's the group I saw. It's a very cool and very Catalan thing to see. That photo was taken in the Plaça de la Vila de Gràcia, which also in the Gràcia neighborhood. It's also pretty close to Parc Güell. 

I worked in Barcelona only for a year, so I don't claim to know the city but if you have other questions, let me know!

Everyone is on the money but I would also just walk as many neighborhoods as you can to feel the complete flavor of the city. Hit up El Borne (lots of hipsters) and go to the top of Tibidabo and have a drink at Mirablau for the best view of the city.

Parc Güell... Casa Batlló.... La Pedrera

Both the Barri Gòtic and Basílica de la Sagrada Família are worth your time. The other area that has great Modernisme architecture (although not off the beaten path) is Eixample. 

I've written a couple of blog posts you might find useful. 

http://destinationsdetoursdreams.blogspot.com/2013/09/walking-in-barcelona.html

http://destinationsdetoursdreams.blogspot.com/2013/10/barcelona-architecture-modernisme-and.html

Hi, in Barcelona you should see every building made by Gaudí. The most beautiful places i`ve seen are the Casa Batlló Parc Güell La Pedrera Palau de la Música Catalana, and you can find amazing buildings pretty much by just walking around. You can also go to the Montjuïc in a cableway, and the Temple of the Sacred Heart of Jesus is mindblowing. Just have fun walking around!