We just returned from Barcelona. Incredible city. Awesome place to visit in January - nothing was too crowded and the weather in mid January ranged from pleasant and sunny to manageable. I'm a bit ashamed that it was my first trip there and that I had no idea it was so awesome. With all the dedicated pedestrian pathways it may be the best city in the world to walk 25000 steps a day. We stayed in the Gothic Quarter for 5 nights. I'd branch out to a less touristy district next time but it certainly was convenient. Sagrada Familia and Palau de Musica Catalana were the highlights. We snagged tickets to a pianist concert and had an amazing time. The acoustics are incredible in the beautiful art deco building, which dates from the early 1900s.
Restaurant recommendations -
A friend strongly recommended Teoric Taverna and we had an awesome experience. The concept is apparently to keep the prices reasonable while serving a "Michelin style" menu. The only choices you'll need to make are between the 10 course tasting menu or the 13 course. I disdain long, drawn out meals but they kept things moving and we were out of there after about 2 hours. The 13 course menu was only 62 euro pp, definitely a great value. Shrimp tartar served on a fried chicken skin cracker was off-the-hook great, as was the venison. Reservations needed.
El Nacional - Four distinct restaurants under the same roof, each with a different style of Spanish cuisine. Plus there's a couple of tapas bars. We had an amazing lunch at the beef-centric eaterie. We didn't need a reservation for lunch in January but ymmv.
Bar La Plata - the concierge rec'd this place for tapas and it's great. From reading internet comments afterwards, some complain it's too pricey. It's not cheap but the quality is definitely there. It's a local's type of hangout and a very authentic, fun place to hang out and eat and drink. Their patatas bravas, the pig trotters with foie gras, grilled artichoke stuffe d with romesco sauce, and the flan were among the outstanding dishes. Even their tomato toast was the best we were served during our stay in BCN.
Also worth a mention is the new Time Out restaurant location. Apparently the concept was so successful in Lisbon they branched out a few months ago to a handful of different cities. The location in Barcelona is by the marina so not that easy to drop into but a pleasant walk from the Gothic Quarter.