Mindlessly quoting Wikipedia, Burgas is the second largest city on the Bulgarian Black Sea coast. Does it really say anything about the place? Not much at all. In my opinion, it is the coziest coastal city in the country. Less busy with cleaner and less commercialized beaches, than Varna. Yet, big enough to always find something to do and something to see. Hotels are plentiful, good, and affordable; so are the cafés, buffets, and street food joints.
Burgas could be the perfect base-camp to explore the Southern part of the Bulgarian Black Sea: Nesebar, Sozopol, and other places. Unfortunately, the direct flights to the capital and back are no longer available. The fastest of the Sofia–Burgas trains takes just over six and a half hours, and the bus ride to the airport in Varna will take three.