Cordoba has Jewish sights, including the remains of a synagogue and Casa de Sefarad, a Jewish museum, and a lovely statue of the Rambam in a nearby plaza. The Museo Vivo de Andalus (folk museum) includes information on the Jews in Andalusia, especially in tandem with the Christians and Muslims. It also has one of the top sights in all of Spain, the Mezquita.
There is next to nothing left of the Jewish community in Seville. I took a 3-hour private walking tour with a great guide (I'll be happy to provide his contact info). I believe he also does tours in Cordoba. It consisted of walking through the streets where important Jews in Andalusian history lived and synagogues used to be. There were only a couple of minor physical remains - a stone or two. That's not to say that Seville isn't worth going to.
The fast train from Barcelona to Seville takes about 5.5 hours - about 40 minutes less to Cordoba. Flying will take about as long since you have to get to/from the airport, allow a lot of time for check-in, security, boarding, then disembarking, waiting for luggage (carry-on limits are likely to be very low). You may save an hour but you'll have all the attendant hassles and discomforts and some additional expenses. The trains are comfortable and the journey's pleasantly scenic.
Another alternative is to spend a couple of days in Toledo. There is a lot of Jewish history there, a couple of preserved synagogues, one with a small Jewish museum. Take the train from Barcelona to Madrid (2.5 hrs), then transfer to the Toledo train at Atocha. Toledo and Cordoba are my 2 favorite towns in Andalusia.
I visited Girona as a day trip from Barcelona. The Jewish museum there is excellent, detailing the history and daily life of Jews in Catalonia.
Other day trips from Barcelona - Montserrat (if the weather's good), Figueres (for the Dali Museum and Jewels), Tarragona (Roman ruins).
If you don't want to use up 2 half-days travelling to Andalusia, consider a night or two in Valencia or Zaragoza. Or take your warm clothes and go north to Andorra for some winter sports in the snow.
There are lots of things in Barcelona itself. Explore the official tourist site here.