Would highly recommend staying at Elena's home if you're OK with not being right in the touristic centre of the city. The home is about a 20 minute walk to the coliseum, or you can walk 5 minutes to the local metro. We walked everywhere from the home, taking the metro only once. Found this to be a great way to explore the area.
The grocery store located down the street has great products to make your own meals, and the kitchen is equipped with anything you could possibly need for the preparation. The kitchen itself is beautiful, equipped with a gas stove on which we made most of our dinners during our stay. Enjoying dinner or breakfast on the terrace was really the best way to start or end our days.
There are many food options within a short walk from the home, if you don't want to cook. If you enjoy Gelato, you must try Fassi, just around the corner - it's amazing!
Elena was extremely responsive and helpful before and during our entire stay - something you rarely experience with hosts!
I would stay at Elena's home again, and would recommend it to anyone who is considering staying in Rome. You will be glad you stayed here!