By public transport it's not really feasible, even travelling by car you're looking to fit a lot in and won't really get much time in any location given the amount of travelling.
Pals and Calella de Palafrugell have to be reached by bus - either from Barcelona (2-3hr journey) or from Girona (about an hour). Girona itself is about 35 minutes fast train from Barcelona - so once you factor in connections and the return journey that would be a lot of travelling. Two out of the three areas might be more feasible.
Eg take the train from Barcelona to Figueres. Explore Figures in the morning, then train to Girona and explore Girona in the afternoon then back to Barcelona. Or take the bus to Calella de Palafrugell and Pals (you'd need to take a taxi between the two as local bus services are very limited). then go back via Girona.
I agree with Saul, not really doable by public transport....and that's a lot of travelling in one day.
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