Go on the tour of Sagrada Familia - it's well worth it. The food market on the Ramblas is great for.stocking up for picnics. Parc Guell is great but start at the top end as it's up steep hills from any transport (get there and then enjoy said picnic).
Changing lines on the Metro can be a 15 min walk!
Picasso museum quite good but the famous later stuff is all elsewhere. Chocolate museum worth going to simply to admire the carvings of chocolate.
Ask in your hotel for recommended restaurants and places for pinxos - mini tapas on toothpicks.
ooh bcn is my most favouritest city metro is very good but if you are pushed for time, the tourist bus is an excellent way to get around and see everything! parc guell, sagrada familia, las ramblas etc.. all lovely to visit as is parc de la cituidella (sp?) and Picasso museum. avoid eating on las ramblas - mostly awful! but there is an amazing indoor food market there if you want a picnic lunch
Barrí Gótic , old quarter is beautiful and has lots to see. Can't go without seeing the Sagrada Familia and Casa Battló. There is also a little fair on the top of Mount Tibidabo , you can get the Funicular tram train up there which is fun depending on how old the family is. Absolutely have to sample the waffles (gofres) and ice cream!