When to use "下一个" and when just "下一" to translate English "next"?
Noun phrases in many cases require classifiers (= measure words). 个 is the generic classifier, but you should use whichever classifier is appropriate. Note that 一 is usually elided from "下一个":


Next month = 下(一)个月
Next week = 下(一)个星期
The next book (e.g., imagine it's a series) = 下一本书
The next photo = 下一张照片


Some words are "their own measure word" in some sense. 天 is really the only one in this category that struck me as weird. The others are words that usually are measure words but occasionally stand on their own:


The next day = 下一天
The next (bus/train/subway) stop = 下一站
The next sheet = 下一张


One word I've encountered optionally takes a measure word: 小时. It's (normatively) correct to always use 个, but in some people's colloquial speech, it (like 天) acts "as its own measure word":


The next hour = 下个小时
Don't think I've heard "下小时", but I've definitely heard it sans-measure-word in other contexts, e.g., "还有三小时" (= Three hours to go!)