As noted in almost all the reviews, this is an outstanding location. With the metro being so close by, what you can't walk to in historic Rome, you can easily reach by public transportation. Within a few minutes' walk were: a pastry shop, gelateria, grocery store, church for mass on Sunday, many fine restaurants and bars, parks - virtually everything. All the most iconic sights are easy to get to.
I liked the coffee machine (Nespresso) -- fantastic coffee in 2 minutes! Also liked having access to a washing machine in the patio, which after 1 week we were ready to use. The patio is a lovely place to relax outside.
Chromecast is a nice touch as well.
The host is a fine young man who is very responsible and conscientious. He was most attentive to our needs and responded quickly to our questions.
I would return to Cortile del Colosseo in a heartbeat and would not hesitate to recommend it as a great location in Rome.