If you're going to Lisbon, I suggest you take some time to visit the Great Lisbon area. This includes the city of Lisbon and its associated towns and villages, but also towns such as Oeiras (this is my home town), Estoril, Cascais and Sintra. Keep in mind that Belem was where boats set sail to explore the world in the 1400 and 1500's, so you'll get a better appreciation of all the monuments, you see and their geographic location. In Lisbon itself, you can start at Terreiro do Paco, get a pass to a tourist tram and just hop on an off throughout the day.

In Seville you can start from Plaza de Espana and choose what you would like to visit from there.

If you are going to Barcelona... I don't even know where to start. Barcelona is awesome whether you like urban, beach, nature, anything. I like to go for a walk on the ramblas when I arrive. They lead to the beaches and the city center, but they are a great experience by themselves. You should definitely try to go to Montjuic and some of Gaudi's places (especially Parc Guell). But again, Barcelona is a world in it self. Also take some time to just sit and relax at one of the restaurants in the evening for a few hours just enjoying the food and wine.

Just to note that when I travel I think it's helpful to start in the main plaza of the cities. There you then have a whole bunch of choices of what to do next. Both Terreiro do Paco and Plaza de Espana are the main plazas in Lisbon and Seville, respectively.

Maybe this was a lot. But hope it helps.