Thessaloniki isn't short of hotels, but for solo and budget travelers, the standard and value look very bad. Hostels are the best alternative, and while Thess Hostel is in a shabby part of town, it's well-positioned for public transport, including trains. Some people might be put off by the surroundings, but I never felt unsafe walking in the street.
The staff, most of all, make this a great hostel. Rooms are kept clean, with regular changes of bedding and towels. The basic layout of self-contained apartments (combining a couple of two-person dorms with a bathroom and kitchenette) makes it feel small and personal. I didn't try the rooftop garden, or the nightly socials, but the reception area has a regular buzz of arrivals/departures, and conversations start easily there with staff and other guests.
It's definitely not a luxury destination, but it fulfills all of the essential needs, and for ten days I felt welcome and well advised on all my questions, and I was never without a cup of tea, which is a plus.
They also have recommendations for places nearby to eat, and famous local spirits, which I didn't get round to trying. But that's as good a reason as any for visiting again the next time I want to go to Greece.