Barcelona - Things To Do

[Corso Marche]

I've a short amount of time to spend in Barcelona, around 30 hours including the overnight/sleep time. So basically 1 and a bit days of tourist hours. I've never been before, but it's likely a safe bet some on here have been.

Any suggestions for the key points and highlights/essentials to fit in?
And also decent eateries, restaurants etc etc

Any stuff of interest to petrolheads in or near the city?
(I did a search and did find the MNACTEC museum and technical centre, but it'll take the guts of 3 hours for a return trip from Barcelona which is effectively a half day lost on travel so that's not an option on this trip unfortunately).