More:~
I have to agree with Barney's description of Rome.
However,it must be said that Rome is not a quiet city,most of the (old) streets are narrow and still take quite a lot of traffic.Many of the (narrow) backstreets) have no pavements,and you have to watch out for both cars and scooters(& watch your handbags!).
Also (thinking of your Mum) Rome is built on 7 hills,so many streets are either up or down hill,and many are still pavementless and cobbled.
There is an underground system,but it's not on the scale of London or Paris,so walking is still the best way to see the city.
If you can find a Hotel with a garden(rare) where your rooms are at the back they may be quieter.
April at least will be a pleasant month(temperature wise).Never consider going to Rome in July/August/ it is stifling.
We have also stayed in this Hotel:~
http://www.hotelderussie.it/
Which is small and boutique like,but again not cheap,bu then no hotel in Rome is what you would call cheap,unless you are way out near the Airport etc.
Personally,from the way you describe it,I would choose another city,taking your Mum into consideration.
One that is flatter,has a better transport system,and is cheaper than Rome,but as I say this is only personal.
Rome IS an amazing,frustrating and inspiring city,and hopefully going in April you won't have TOO many tourists to put up with?
Like Barney I never felt unsafe anywhere in Rome,the Italians are larger than life and very friendly,especially if you have even a few words of the language.
I hope I haven't discouraged you,I just thought I would throw a few sugesstions into the pot.
I also agree with BArney about getting hints from TripAdvisor.com an excellent site.
Buone vacanze!