We stayed at Giovanni's apartment with my mom, and we loved it. It was perfectly clean and had everything inside. The apartment building is relatively new, and has an elevator, so 3rd floor was just fine. The apartment is sunny and spacious enough for two people. It located 5 min away by tram from Policlinico metro station. Termini station is pretty far by foot – around 20 mins. So if you feel fine walking or using public transportation, it should work. The area is typical for train station surroundings – not very clean. There're supermarkets (even 24/7) and lots of different restaurants nearby.