the bounce around thing might seem good on paper, but it means too much time in transit. One city is fine.

You can get to Toledo, Barcelona, Cordoba, Sevilla, Cuenca, Valencia, etc. in a matter of hours.

from city to city (its too much work).

I prefer to park myself in a central hub and day trip outward.

Madrid has a lot but Barcelona should not be passed up. The two cities are very different. Could you do two cities?
You could also stay in one city and take day trips. From Madrid, you could go to Toledo. It is very touristy but if you like art, it has a trove of El Grecos. I don't know what would make a good trip from Barcelona.

BTW, I really enjoyed Spain and I think you will love it.

Barcelona, Barcelona! BUT, you can easily take the Eurorail to Madrid for a day or two. Or least for the Prado.

but even with day trips to the surrounding areas you could stay in one hotel without being confined to one city.
As for one location, Barcelona was a very nice, vibrant city when I was there.

Also, be careful when people approach you out of the blue even if they pretend not to sell anything or if they want to do give you something like a rose. That's what happened to our family. Old woman giving us a rose and pretended she only wanted a small coin. Instead, she quickly reached into the wallet for the bills and got only caught because so much else was in the wallet.

but you need at least 3-4 days to thoroughly enjoy Barcelona....so that only leaves time for a day trip or two, which would be Madrid and perhaps a trip down the coast.