Trains in Italy are running kind of normal. Check the timetables on www.trenitalia.com. Occupancy in long distance trains is limited to 50%. There are many cities worth a visit, too much for one holiday...

Recommended stops depends on your interests… nature, cities?
Most popular stops for Interrailers are Venice, Roma, Florence, Cinque Terre.

I’d recommend you to go further South and get to Matera (last train from Bari is not included in Interrail but it is really cheap) if you have time. Also Amalfi coast is nice but it is really pricey… maybe not suitable for a backpacker trip . Also Lecce is definitely worth a stopover if you make it already so far to the South.

A female friend used Couchsurfing in Italy this June and enjoyed her stay. As a girl it won’t be a problem to find a host, but check the profiles careful. There are enough guys on couchsurfing who think it is some kind of tinder ^^.