also: てんきそうだんしょ
noun
weather bureau; weather consultation office
A facility or office that provides weather information and advice. Often used in official or institutional names.
地元の天気相談所に電話して、明日の天気を確認した。
I called the local weather bureau to check tomorrow's weather.
気象台 is a meteorological observatory, often a larger government-run facility, while 天気相談所 is more focused on providing weather advice to the public.
Compound of 天気 (weather), 相談 (consultation), and 所 (place/office). A straightforward modern compound.