Just returned from two days in Barcelona - Jan 7 & 8, 2010. I would suggest that you purchase tickets to the tour buses that run routes throughout the city on double-decker buses. You can get on and off at a variety of stops on both of the routes. I believe there is a third route that is aso operated in warmer weather. In any case, the tours give you a good overview of the city.
As far as must-sees, I would suggest the cathedral that is being built based on a Gaudi design. Also, make sure you walk the Ramblas, a large pedestrian street that runs from one of the major squares down to the sea. Very intereting with lots of shops, restaurants, markets, etc.
We definitely would like to go there again, One or two days are definitely not enough time to spend in that city.
You are wellcome in Barcelona, actuially there are many things to in Barcelona. however one day is too short to see all Barcelona, I invite you to take a Segway Tour to explore the most of the city.