I am not sure what your age has to do with traveling to Spain, as the country is a great destination for those of all ages.
There is so much to see and do in Spain that the list is almost endless. You can be as active or as sedate as you choose, depending on health, fitness, and energy. I have been to all the places you enjoyed, and they are all pleasant, but I always look for what is unique about each place where I travel, and I certainly do enjoy large cities as well as small medieval towns.
For me Spain is more than just a country with tourist places to visit--it is a vibrant historic nation with a lot of passion, art and history, and my heart is always happy as soon as I start hearing "Castellano."
We do not do full guided tours, but we definitely take day trip tours when our time is more limited, and there are some great tour ideas with companies like Walks, who we often use.
We have driven all over Spain, as well as taken trains everywhere. As we often have larger suitcases these days, we avoid local public transportation and take taxis. When we were quite young we had backpacks, and even a tent!
Going in mid-April means most of the beach locations will be too cold for swimming anyway, bit it is certainly a pleasure to stroll on beaches.
Well, I would strongly recommend lovely Sevilla as a place for you to visit, but Easter is April 20th, so the city will be extremely busy if you arrive near that time, as it is the center of many celebrations.
Madrid is a very large city, quite cosmopolitan, and very active. The museums in the city are world famous, and of course, there is the Royal Palace to tour. People watching in found in the Plaza Mayor. Near to Madrid with pretty easy access are the smaller and extremely historic towns of Toledo, Segovia, Salamanca and Ávila.
Barcelona is full of tourists these days, but the architectural wonders of Gaudí make the visit worthwhile. Train travel between the two large cities is very efficient and reasonably priced.
I strongly doubt you will encounter any protests in April, as the high travel season will not yet be underway.
Have fun planning, and have a wonderful trip. Buen viaje!