I bought a one way ticket from NYC to London from Ukrainian International Airlines for 391 USD.
I flew into London and bought a round-trip to Barcelona from London (ahead of time).

This is a break down of what you can do in Barcelona if you are there for a very short period of time.
In my case, I was here for a wedding!

Barcelona!
2.5 day trip (4 days but not really).
June 24th @6pm – June 26th @6am
Airplane: Ryanair to / Ryanair from
Bought tickets months before the trip.
Total: 199 GBP Roundtrip (including a paid checked bag – damn you ryanair)
Journey: 2 hours and 15 mins

Accommodation: Twentytu
Cost: Four bedroom= 30 Euros a night per person (with breakfast).
Great affordable alternative to a hotel. The hostel was clean and well maintained.
10 minute walk to the beach and 30 minute walk to Plaça de Catalunya.
I recommend staying here if you are on a tight budget.
Cost of taxi from the airport to Twentytu was 35 Euros

Friday, June 24th
Dinner: Mirablau
Address: Plaza Doctor Andreu s/n 08035 Barcelona
Cost: 135 Euros for 5 people (All together)
The views are to die for and the food did not disappoint. The only HUGE downfall was that it was almost impossible to catch a taxi at night. Make sure you have a reliable taxi number to call at the end of your meal.

Saturday, June 25th
Las Ramblas, La Boqueria and the wedding

Wedding

Sunday, June 26th
Sagrada Familia
Must see. Do it.
You can easily grab a coffee and watch the view from afar.
Port Olimpic Beach
Font Màgica
Show times: 21:30, 22:00 and 22:30.
Plaça Espanya
View from the restaurant over looking Plaça Espanya.
Dinner: MasQMenos
Address: Rambla de Catalunya 2-4, entlo · 08007 Barcelona (Spain)
Cost: Set dinner special for 23 Euros per person
Thoughts: Decent food. Good price. Great views.

Departed Monday, June 26th @6am to London!
Cost of taxi from the hostel to the airport was 35 Euros

Next adventure, London!