Since you indicate that there may be a number of nights, then nights is the correct form. If they decided to only provide one night, that would be said, one night's accommodation (the accommodation of one night).

The correct usage depends on whether the phrase is acting as a compound adjective or a possessive noun. If you are using it as an adjective to describe the stay, it should be "a two-night stay" (singular and often hyphenated). In this case, "two-night" modifies "stay," similar to saying "a five-mile run." If you are expressing that the stay lasts for the duration of two nights, you would use the possessive form: "two nights' stay." Without the apostrophe, "two nights stay" is technically a sentence fragment (meaning "Two nights remain") rather than a descriptive phrase for a hotel booking. In the travel industry in 2026, you will most commonly see the adjective form—"Book a 2-night stay"—on websites and in confirmation emails because it is concise and grammatically standard for marketing. When writing formally, remember that if the number comes before the noun it modifies, it stays singular (two-hour, ten-dollar, two-night); if you are talking about the plural units of time, use the plural possessive (two hours', ten dollars', two nights').