Have a peek inside the Born Cultural Center (it's free) where you can see the remains of the city when it was called Barcino. If there is no mass going on, visit the inside of the Basílica de Santa Maria del Mar.
It's best to start this tour after 10 am when most shops open. Smaller shops like La Seu will close for lunch.
Please see opening and closing times for all the spots below:
Monday-Thursday: 9am-2pm, 3:30-8pm
Friday, Saturday: 9am-2pm, 3:30-8:30pm
Cafés El Magnifico Roasters
La Botifarreria de Santa Maria
Tuesday-Friday: 1-3:45pm, 7:30-11:30pm
Saturday: 1:15pm-3:45pm, 7:30-11:30pm
Monday-Saturday: 10am-3:15pm, 6:15pm-11pm
Swiit Ice Cream
Formatgeria La Seu
Monday, Sunday: Closed
Tuesday-Saturday: 10am-2pm, 5-8pm
Beware of pickpockets, they are stealthy but not dangerous.