Hi Karolina,
You can use, literally, "déjame saber"
Let me know what time you will be arriving at my place? - Déjame saber a que hora estarás llegando acá?
Let me know if you want to join us for pizza? - Déjame saber si quieres unírtenos para la pizza
But, as some others mentioned before, you can also use "Dime", "Avísame" or even "cuéntame".