A fish eye or ultra wide angle could be very useful. There are several amazing buildings such as "Casa Batlló", "La Pedrera", "Mercat de la Boqueria", "Sagrada Familia", "Liceu", "Palau de la música".... and also "Parc Güell" that requires a nice wide angle lens to fit as much as possible into the frame.
For sure the 24-105 it will be very useful, and if you have to save space, you could skip the telephoto lens.
In the oldest area of the city, streets are very narrow; again, wide angle is very welcome but the TS-E could be perfect.
I live in Barcelona, and in my case, the most used lenses are: Sigma 12-24 and Samyang 14mm.