Alexandroupolis is a small town with a harbour and an airport. Though the Lonely Planet describes it as "dusty", it has a rocky beach, and a typical Greek nightlife.
There are several trains from Thessaloniki. Slow trains take 6h (9€), fast ICs take only 4 1/2h (16€).
National Network of Buses or KTEL operates a frequent schedule of buses to all the major cities of the country. Shutle buses depart twice daily to Athens (approximately 8–9 hours) and there are hourly connections to Thessaloniki.
OSE, the national train operator, has set a daily bus shuttle to Istanbul that departs the main station early (around 7AM) every morning. Tickets are usually easy to find and can be booked in the ticket office.
There are no cheap youth hostels, but a couple of mid-range hotels by the seaside. Backpackers often just stay at the beach near the train station.