There are many new hotels in the city. Most of them offer BB for a reasonable price.
You can also stay in the suburb called Sarafovo. It has pretty seaside view and easy access to the city centre with public bus line 15 in 20 mins and the airport 5 mins. Sarafovo has numerous hotels. holiday apartments and guesthouses, as well as shops, restaurants and a serviced beach. It offers a good combination of peace and tranquility with easy access to the bustle and nightlife of the city centre. However keep in mind that the taxi to/from the Burgas city center may get a bit experience.
List of many means of accommodation in the city is offered by the Travel Information Center (http://www.tic.burgas.bg/...) at the Burgas Municipality - 2 to 5 star hotels and shared rooms.
If you need something off the beaten track you can also try the private homestays. Especially in summer many old ladies or gentlemen offer accommodation in their houses. If you get off the train or the bus, you will spot their cardboard signs. Some language barriers exist as not all of them speak English. Usually they are hospitable and are a good equivalent to hostel accommodation. If you understand each other and have a good host, sometimes they will prepare a traditional breakfast.
Yonat Hostel
Little pretty hostel well located in the centre.
Apollon Holiday Apartments
Comfortable furnished, brand-new self-catering apartments near fine sandy beach and Aqua Park.