Italy + More

When I stayed in Rome, it was just 2 blocks or so from the Termini.  Yes, it was a bit sketchy.  My younger sister, bless, saw a man peeing outdoors.  But, we never were out at an extreme hour and we NEVER feared for our safety.  Our hotel was fine, as well (not a hostel though).  It was extremely convenient and I had no complaints about it.

There is no "Eurail."  The Eurail pass is simply good for travel on the trains in each country the pass covers (each country generally has a national train service - like Amtrak (except much better) - and certain countries also have private train services).  You need to do your research on each country's national train service website and see how much tickets between your select destinations are.  Eurail pass holders usually still have to pay for reservations on certain trains, supplements for other (I think maybe the Pendolino in Italy falls in that category).  You'll have no problem traveling between major cities. 

There is an Eurail Global Pass which allows for unlimited travel on the entire rail network of 21 different EU countries