Good for you. You've made an excellent choice in Barcelona for your in-depth exploration. It is a really wonderful place.
--The hop-on hop-off busses run in two routes and are very good. Hint: they sell two-day tickets good on both routes. We took both loops completely around the first day, then went back and hopped off at places we wanted to see more on the second.
--Eat lunch at the 4 Cats restaurant. ("Quatros Gatos" I guess).
--Really explore the old city inside the Roman walls. Quite something.
--It's OK to laugh at the Gaudi church (still being built and probably always will be). It's very funny. (This is your architect. This is your architect on drugs.)