I like the Hotel de Russie best for location, and they have a beautiful garden courtyard that is wonderful for an outdoor lunch on a nice day. You need to get at least a deluxe room, and higher category is better. Also I suggest overlooking garden vs street.
Second favorite is Hassler on top of Spanish Steps. Hotel Eden is nice but must get higher category room as rooms can be quite small. It has a great restaurant, but so does Hassler. Hassler IMO a bit more convenient location but Eden nice too. I would rate1. De Russie 2. Hassler. 3. Eden