Rome can be very cheap if you want it. Plenty of economical hotels. Many of the sites are outdoors and free. Food doesn't need to be expensive.

Madrid tends to have cheaper hotels but the admissions are often much higher.

I am just happy everybody has a different favourite. Can you imagine if everybody would go to the same place?
Any city you will choose will be a new experience, so go and enjoy! I believe it will not the last time you will be in Europe.