SELECT room.id FROM room LEFT JOIN busy_dates ON id_room = room.id AND date_to < "04.01.2017"

SELECT room.id FROM room WHERE id NOT IN (SELECT id_room FROM busy_dates WHERE date_from... AND date_to...);

 id              id_room      date_from          date_to        
 -----------------------------------------------------------
| 1          | 10          | 2017-01-03 |    2017-01-07   |       
| 2          | 10          | 2017-01-18 |    2017-01-21   |
| 3          | 10          | 2017-01-23 |    2017-01-27   |
 -----------------------------------------------------------

SELECT room.id FROM room WHERE id NOT IN (SELECT id_room FROM busy_dates WHERE date_from <= "2017-01-04" AND date_to >= "2017-01-06");

SELECT room.id FROM room WHERE id NOT IN (SELECT id_room FROM busy_dates WHERE (busy_from <= :busy_from AND busy_to >= :busy_to) OR (busy_from >= :busy_from AND busy_from <= :busy_to AND busy_to >= :busy_to) OR (busy_from >= :busy_from AND busy_to <= :busy_to));