First out, hostels in Italy aren’t as rife as I’ve noticed there have been in, say, Germany. There is less choice and all-round lower quality.
Livi found a cute place in Verona called Sleep-Easy – it’s in a slightly dodgy out-of-town area but all in all not too bad. No bar or guest kitchen, and not much in the way of atmosphere, but there was a paddling pool… €25 per person per night is hardly a bargain though.
We travelled to Garda by train, arriving at Desenzano, the main station there. The tourist office told us the nearest Garda hostel was in Riva del Garda on the north coast, two hours by bus. We managed to get a room; the hostel, another youth hostel, was cheap and about as central as could be, but lacked atmosphere. We stayed two nights, really enjoying the area.
We got an early bus to Breschia and a train from there to Milan – train travel is cheap if you opt for the less fancy, slightly slower services. Bus travel also.
In Milan with no where to stay, we consulted TripAdvisor only to be horrified. It seemed that every hostel had some kind of pest infestation, sewage problem or was well out of town. Taking a risk, we chose Zebra Hostel, a short (10 mins or so) walk from the Duomo. It wasn’t the cleanest and the bathroom was a bit of the state but it had a great downstairs area with a bar, music, table tennis etc. and we met loads of people there; a great place to stay in the end, so we were there for three nights!
One day we spent at Lake Como, getting the train from Milan’s central station, though the train that goes from Cadorna takes you to a more central Como station. Make sure you get on the slower, far cheaper trains rather than the high-speeders, if that’s in your interest.
Out of Milan heading north, there’s a coach to Zürich, and also a direct train, though this is far more expensive (we were to discover)!