The only 'must' is Tickets Bar. Unfortunately you have to book 60 days in advance, but I really recommend you to try it if you are a lover of food.
Notice that it is not possible to book sooner than 60 days prior to the date, and when the date preferred goes on 'sale' they are usually reserved
within 1-2 days. Even the price is moderate. We ate 16-18 courses with drinks and wines and paid 60-70e / person.
http://es.bcn50.org/
But considering it's your honeymoon, I might suggest 41 degrees that operates in the same premises. 41 courses of food/drinks that are sort of
synchronised with audiovisual elements.
http://www.41grados.es/index.php#/home You will never forget the experience.
The restaurants are managed by the Adria brothers. Check Ferran Adria or El Bulli from Wikipedia if you like. El Bulli has been chosen five times as
the world's best restaurant. A couple years back, Adria closed the restaurant and opened a "simple" tapas bar (Tickets Bar) with his brother.