i am not sure where on the Via Veneto the Luna Baglioni is located, but the street is not that long.
One end of the Via Veneto is the entrance to the Borghese Gardens (top of the hill) and the other end is Bernini Bristol.
The first hotel we ever stayed at in Rome is the Excelsior. It's closer to the top of the hill.
That area is mostly, restaurants, bars and night life. There was no place to buy a Diet Coke or a bottle of water.
The Bristol is on a square and there is a drug store, convenience store (they sell arancini / rice balls to go...not that I know first hand or anything <cough cough>) restaurants and some other convenient stuff.
Coming out of the Bristol and turning left will take you to the Trevi Fountain and the Pantheon ( one of the coolest buildings in a city of cool buildings).
The two are not that far apart, but if you are walking to these things....going home is uphill. that might not bother some.
Rome has a great Hop / Hop off bus tour. You pay one price and you can get on and off any of the busses that are EVERYWHERE. The busses do the "monument loop". We did it and stayed on the entire loop. It was a great way to see a lot in s short time. I want to say it was 20 euros per person. It's been a while.
There is a Hop on/Hop off stop in front of the Bernini Bristol.
I love the location of the Bernini Bristol...so thats my opinion.