Kathy-
We stayed at Hotel Due Torri in August and had no problems. We were out until midnight or 1 AM most nights and never felt unsafe in the area. It is about 5 minutes from the Pantheon and Piazza Navona, but the immediate area is very quiet. Being able to wander around at night was one of the highlights of Rome for us. The extra cost of staying in this area is well worth it.
The downside is that public transportation is not as convenient as in some other neighborhoods. We walked to most places directly or walked to the Spagna metro stop (about 10 minutes walking, a few more with luggage). Walking to the Vatican took about 15-20 minutes depending on where you are going. It’s about 30 minutes to walk to the Colosseum/Forum area and about the same if you take a walk to Spagna and then take the metro from there. It’s also a cheap cab ride from Villa Borghese (about 10 euros).
We did not hear a barking dog, nor were we bothered by the auto shop, but we were in a room with a terrace on the top floor. Both of us would be happy to stay there again, but I think that I would stay in a room without a terrace. The terrace rooms are considerably smaller than the doubles on the lower floors.
We found that reception here was particularly helpful. If you have more specific questions, please feel free to send me a personal message.