how many nights
Used in questions or expressions of uncertainty about the number of nights.
How many nights will you stay here?
some nights; several nights; a number of nights
Indicates an unspecified but relatively small number of nights. Often used in narrative or descriptive contexts.
I had several sleepless nights in a row.
幾日 means 'how many days' or 'some days', while 幾夜 specifically refers to nights.
幾晩 is a synonym for 幾夜, but 幾夜 is more common and slightly more literary.
for several nights; night after night
Compound of 幾 (iku, 'how many') and 夜 (yo, 'night'). The reading いくよ is a straightforward combination of the two elements.