Florence and Cinque Terre

Hi Judith. 1. There are two hostels in CT, at Corniglia and Manarola. They both get generally good reviews. You can google them or try trip advisor.
2. Yes, simplest fastest route is via Milan; about 5 hours. Use trenitalia.com to see routes, times and fares. Enjoy your trip!

Judith, As the previous reply mentioned, there are Hostels in both Manarola and Corniglia. There are also some private rooms in Riomaggiore and other towns, which are very reasonably priced. You might have a look at Mar-Mar Rooms, as they rent both private rooms and also operate a Hostel of sorts. One point to note is that many of the private rooms don't include breakfast, so you'd have take care of that on your own. The Ostello 5 Terre in Manarola has been around for many years, and is clean and well run. However, note that they have a STRICT Lockout in the afternoon for three hours, and the doors will be LOCKED. The Corniglia Hostel is relatively new, but seems to be getting good ratings. Corniglia is not as popular as the other towns, as it's located high on a rock bluff so not close to the station, and the boats don't usually stop there. However, there is a Shuttle Bus that has regular service, and walking down the stairs to the station is not overly difficult (going uphill is another story). There's also the famous (infamous?) Mama Rosa Hostel in Riomaggiore, but the reviews don't exactly seem "stellar". Mama Rosa is often waiting in the Piazza at the station, hoping to "hook" a few guests for the Hostel. There are fairly frequent trains from Manarola to Verona, most with changes in Monterosso and Milano Centrale. Your destination station will be Verona Porta Nuova. and travel time will be about 5H:15M. Some of the trains on that route are Regionale (DON'T forget to validate your ticket) and some are Freccia (fast) trains (reservations compulsory, which are specific to the train and departure time - you can't just board "any" train). Happy travels!

We really liked the Hostel Archi Rossi in Florence. Near the train station and very safe. They have dorms and private rooms with en suite in their "Annex".