Can't disagree with the hotel suggested already, and also that area.
Rome is actually a fairly small city and it is possible to walk around and see most of the sights. There are also plenty of buses and taxis as it might not be so easy for someone of your Mother's age and it could get hot in September.
The streets, buses, tourist areas, etc. can get extremely busy and you have to be wary of beggars, pickpockets, etc.
Have a look on sites such as trip adviser, late rooms, etc. for guest feedback, availability, pricing, etc.