Rather than saying that 两 is used with nouns, I would say that 两 is used with measure words, e.g. 两个人、两本书、两棵树. If you use a measure word along with the number 2, use 两.
两 is also used with numbers that are larger than 100, e.g. 两百， 两千三百六十二. If it helps, 百 and 千 can be seen as a sort of measure word.
两 is used for telling time, e.g. 下午两点. Again, 点 functions as a type of measure word here.
二 is used when counting without measure words, such as in telephone numbers, metro lines (二线), addresses, etc.