Uber works differently in Rome.
A search of this forum will bring up some threads about it.
We just take cabs- they are not too expensive. Have your hotel call for one or go to a taxi stand. They can be found near every major sight/monument.
Here is a list:
https://www.livitaly.com/find-taxi-stands-rome/
They are all supposed to take credit cards but check before you get in! The rides we have taken have all been about 10 euros so we usually just pay cash- that way we have control.
We've really only taken to/from train station and over to Vatican.
Rome is very walkable- as long as you are staying somewhere in the historic center you can walk most anywhere. We prefer the area near Pantheon/P Navonna/Campo de' Fiori.