The old town for free
Half the Gothic Quarter and El Born works as an open-air museum; you only pay if you step into a ticketed building.
The Cathedral from outside
The Gothic facade and the cloister with its thirteen white geese are the best part, and both are admired perfectly well from the public side.
Gothic Quarter lanes
Plaça del Pi, Plaça Sant Felip Neri and the stretch of Roman wall by Plaça Nova ask nothing but shoes and an hour.
El Born and the Call
The old Jewish quarter and the medieval lanes around the Basílica de Santa Maria del Mar are free to wander at whatever pace you like.