I would highly recommend the Hotel Morandi Alla Crocetta www.hotelmorandi.it The location was great and the service excellent. We had a very large room. You can read a review on the Mini Travel Guides on this website as well.

I just went through the exact same analysis. For Rome, I ended up choosing the Daphne Veneto (www.daphne-rome.com). There's a 10% discount if you pay in cash. For Florence, I chose the Hotel Davanzati (www.hoteldavanti.it). Both have received glowing reviews, are very service oriented, are in prime locations, and within your budget.

Good luck!

Davw