We did a bike tour in Barcelona last spring and it was great - very informative and a fun/quick way to get the lay of the land. You have a lot packed into Barcelona; you may have to cut back there? Every place you visit will be very busy! Barcelona will also have many options to eat vegetarian and other types of food, whereas Seville will get more limited, as it is much smaller. Consider a Flamenco show in Seville.
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