Helpful staff, clean pool, protected area.
There are several amenities for small children around (enough for 3-4 days): several water parks, burgas sea beach with bikes and hoverboard rental.
South of Burgas there is ravadinovo castle, boat on ropotamo river, Poda Protected Area.
If needed, Varna (2 hours drive) has dolphinarium, cartings and amusement park.
Rental car is a must though.
Just don't go to sunny beach, anything near it has price twice as high as other places. As basically anything that has english letters on it :)