Arriving before check-in time, what to do with luggage?

You could try emailing that question directly to the hostel. Otherwise, if the city or town has a large train station, it may have lockers or a left luggage counter.

Sarah, Could you provide a bit more information? Which Hostel are you staying in? I can't comment on all Hostels, but many will store luggage in a separate area until check-in time. As you'll be staying in a Hostel, be sure to pack a small but robust Padlock for the Lockers. DON'T use a Luggage Lock as they're simply not secure enough.

Like Ken says, many hotels/hostels will let you store your bag til check-in. Usually though, it's not in a secured location, but in a back room somewhere. I second (third?) the suggestion of emailing the hostel and asking. You might also be able to ask for an early check-in. Another option if the hostel has no luggage room and/or there is no train/bus station nearby, might be to find a hotel that would be willing to store your bags for a small fee.

I would opt for a train station. It's worth asking the hostel if they have a place to store your stuff until check in. Even if they do, I wouldn't take advantage of it unless it was a room with individual lockers you can put your own padlock on. Hostels are good places to stay for basic budget accomodations. They are notorious, however, for petty theft. I wouldn't leave my stuff out in my own room unless I was physically present. Leaving your bags in a room where others have access while you aren't around is too big of risk.

"They are notorious, however, for petty theft." To expand on that thought, theft can certainly happen in Hostels so a few precautions are a good idea. Most Hostels these days provide Lockers, but guests have to provide their own Padlock (which is why I suggested the OP to pack one along). I've found the construction of Lockers to vary somewhat between properties. Some are a very good steel construction, while others are somewhat less robust with a somewhat "flimsy" locking mechanism. I'd strongly recommend using a good quality Padlock with "heel & toe locking" (purchase from a Locksmith rather than the local discount store). It shouldn't be overly large, as the mechanism on the Lockers will only accept specific sizes. A rekeyable Padlock provides better long term flexibility. The smaller versions of These Padlocks are one type that I would use. It's also a good idea to secure Backpacks in some way both in storage areas and in Dorm rooms (which is why I prefer a panel-loading Pack over a top-loader). While it only provides a "basic" level of security, it's better than nothing. One Hostel that I stayed at in Rome on my last trip also had Lockers in the Baggage storage area, which was a nice touch. I had no concerns about leaving my kit there while I went out to get some lunch. Cheers!