Can a doorbell transformer be installed outdoors in a protected location?
None of the doorbell transformers I have used would be code compliant outside. Your 120v junctions would be fine inside the box but the transformer and low voltage would be exposed. The NEC requires us to install electrical equipment according to its listing 110.3.B. If the transformer is protected and the low voltage and line voltage are separated with barriers it may be possible but normally I would say NO.