Tom, I had to laugh at your many details. Thanks! Ok, my recommendations:

You mention a place called The Regent in London for the very low (for London) price of 120 USD a night. This could be the infamous Regent Palace and I would caution you to look twice. This place has disappointed so many travelers. For me, the best thing for London is to use a discount booker. Ziners and I have had very good luck with www.autoeurope.com and www.abouthotel.com.

Rome: Many Ziners like the Hotel Delle Muse. I like to be near the via Della Scrofa, where my favorite bakery is, so I like the Hotel Portoghesi

http://www.hotelportoghesiroma.com which may be just above your price range.

Anyway, these are my recommendations. I hope they help. Ciao, Debbie in Pittsburgh