Hi, I think there is a good chance you guys will be pretty tired especially if arriving in the afternoon. My recommendation would be to just walk around the neighborhood to get the lay of the land then grab something to eat before heading to bed early.
There are typically 4 kinds of restaurants (not including fast food) in Spain:
Bar-Restaurante - these low-key establishments are frequented most by locals during the weekdays. They usually serve a 'Menú del día', an excellent seasonal three course lunch. Here one usually sits one's self on the outside sitting unless there is a reserved placard on the table. The waiter then comes over to see what you want if just drinks or food as well. The waiters will check in on you from time to time, but can be considered slow compared to American standards. These are usually only for lunch.
Restaurantes - more upscale affairs with table cloths, wine menus etc.. Here there is typically someone you talk to first to get seated (like a host in the USA), they usually will be standing near the entrance. This is most similar to the US in terms of service. These are usually for dinner, starting after 9:00 pm.
Tapas bars - these places are usually located in the more touristy centres of cities and will have long bar tables with different tapas on top, here you usually make your way to the bar first and talk to the bar tender directly to get service or if you want a check, waiters will not come to you here, you have to be more proactive. Don't expect Tapas to be cheap eats, they can get quite expensive as you add them up.
Gastronomic food markets - these are where local restaurants have food stalls located in the main market, that sell street food to eat on site. These newer types of food markets have become quite popular in Spain in recent years, especially for those looking for a quick drink and a bite to eat. You just order what you want at the counter then sit down at any empty table then pick up the food order when its ready and eat at your table.
We eat dinner after 9:00 pm in Spain, so probably your best bet to find something open earlier would be a Tapas Bar, you don't need a reservation for most tapas bars if you're eating at the bar, eating at a table will sometimes be more expensive and more difficult to secure seats. The better Tapas bars tend to be around El Born and El Poble sec, I can recommend Bar Celta Pulperia and Quimet & Quimet in those respective neighborhoods.
PS: Be careful to not wander into El Raval, it's a seedy neighborhood with narco-trafficking and prostitution and easy to get lost in at night. I only mention this because it's right next door to the Gothic Quarter and some unfamiliar tourists might not know it's a no go place at night.
