Just some thoughts about hotel location and walkability.
Rome
We recently went back to Rome in fall of 2016 for a few days pre-cruise and I found it a lot more walkable than my last full visit in 2003 (perception-wise). The missus had been there more recently than our 2003 and recommended doing a lot of walking but I think a lot had to do with Google maps and being able to get a handle on our bearings and where we were heading.
On our most recent trip, we stayed about 4 blocks northwest of Termini station and found it fine. Walking around the station for night time walk, the only areas we found somewhat sketchy were in the train station itself and in and around the McDonalds across the street southwest of Termini.
The areas has cheaper accommodations and obviously has easier access to the train station and bus loop in front of it. But it is further walk from some of the key sites. But we did manage to walk from as far as the Vatican and Trastevere areas back to the hotel and found it quite a reasonable walk.
The most central point for all the main tourist sites is likely around the Pantheon area.
I'd also recommend using the bus system if you have access to mobile data and google maps. We found Google maps really good in terms of bus routing. You get to stay above ground versus taking the metro.
Florence
We normally stay northeast of the train station and walk south to the heart of the tourist areas.
Yeah, the train station can feel a bit sketchy here too. Seemed to be a number of homeless sleeping in the station.
Very walkable as the tourist core is generally car free. We haven't stayed south of the Arno but would consider it as it's an easy walk north into the tourist areas.
Venice
We've stayed once near the train station and once deeper in.
Google Maps is also great for navigating the alleyways.
For a future trip, I would consider staying on Lido island because it's cheaper and there is night service vaperettos, though I'd be concerned about service issues.
Italy tips
Validate your transportation tickets before boarding.
Research strikes before your trip. Italians seem to love to go on strike planned weeks in advance.
Paris
We used to stay in this hole in the wall in the 1st near the Louvre but they reno'ed into apartments. The metro is pretty extensive so I'd be more flexible where we'd consider staying. However, we'd still likely want to stay in the lower numbered arrondissements. There are still some areas feel a bit sketchier after dark.