Here are some places we've stayed in the last two years and really liked, Kate. Don't know exactly what you mean by "relatively cheap," but all just over 100 Euros per night, or thereabouts, including breakfast in most (and all are centrally located, FYI):
:Madrid: Hotel Europa, just off Puerta del Sol
:Barcelona: Catalonia Albinoni, just off Placa de Catalyuna
:Venice: Locanda al Leon, near San Marco
:Florence: Pensione Alessandra, near Ponte Vecchio
:Roma (this is the only one that's a splurge hotel, over 200 Euros, but it's AMAZING): Residenza Cellini
All of these are in RS Italy or RS Spain, FYI, both of which would be great for you to acquire and read. Also, you can visit my blog with restaurants and itineraries for all of your cities (except Paris, to which I've never been). It's located at http://moltogentileitalia.blogspot.com. Good luck!
EDIT: These were all doubles with private bath, FYI.