Don't worry about race. Everyone will view you as American because your dress, talk and mannerisms will peg you as one of us (whether you like it or not). They don't speak Spanish here either (except as a second language), Catalon is their language and they don't expect everyone to know it, so don't worry too much about it. We found most people either knew English or together we could figure out what we were talking about.
I think three full days is a good visit to Barcelona though you could find more to do if you had more time.
Day one will be to get over jet lag. Walk the Ramblas down to the beach, then up the beach and just enjoy outdoors in the sun and relax. The beaches aren't the best but they're okay. It's best to sleep on the plane then stay up till a decent bed time on the first day. Having had kids in tow on European trips, expect at least one of your kids will do anything but sleep on the plane, then be out on their feet day one, fortunately kids bounce back fast so by day two they should be fine.
I like to spend a day just in the Gothic Quarter. Start with a guided walk from the TI in James I Square (or the Catalon version of that). Then start visiting the sights that interest you. It's easy to spend a full day there.
Another day is good to see Moderniste architecture. The style is unique to Barcelona and should be seen. Three main sights can be seen in a day, the Block of Discord, Park Guell, and La Sagrada Familia.
The third full day could be:
- A day trip to Montserrat (great hiking),
- A train ride up the coast to visit a nice beach area (Arenys de Mar is one choice but you could get off at any of the small towns along the coast).
- Visit some of the more well known stops up the coast, Girona and Figueres.
- Visit Mt. Juic in town
or other options.
You have to look at the options and decide what appeals to you most.
