Hello.
Enric might be able to give you some specifics about Barcelona, but I can recall several fantastic meals at the tapas bars in El Born. I particularly like the Euskal taverns, where you just walk up to the counter and pull off whatever you want.
For Granada, most places on Calle Navas are the place to be. The great thing about Granada, along with many bars in Madrid, is that tapas are free with each drink.
Sevilla-do not miss the Alameda de Hercules, which is a pleasant row of shops and tapas bars, with plenty of outdoor seating. It is off the tourist path, but definitely not far from the main sites. It's a 10-15 minute walk from the cathedral, and well worth it. HOHO buses have a stop there.
My favorite neighborhood in Madrid is La Latina, and the bars on Calle Cava Baja do not disappoint. I especially like Restaurante La Camarilla y La Colchoneria at Cava Baja 21 because they have craft beer. Don't forget to get a bocadillo de calamares off Plaza Mayor-La Campana is a solid choice.
The Lavapies neighborhood in Madrid and the Albayzin quarter in Granada are great places to enjoy some time away from jamon, which everybody needs now and then.