In Japanese, grammatical clauses are generally marked as such by adding a specific particle at their ends.
For grammatical subjects, that particle is が. In your example sentence, the subject noun is 雨. Therefore the subject of your sentence is 雨が.
Note that this is a tightly coupled single lexical unit. In other words, you cannot just insert stuff (like 明日) in-between the clause head and its particle: "雨明日が" is nonsensical (a blatant syntax error) from the point of view of parsing the Japanese language.
That said, as long as you don't separate particles from their clauses, Japanese is quite flexible in allowing you to swap things around: "雨が明日降るよ" is a valid (if slightly odd) alternative. (With this word/clause order, the emphasis is more on 明日 than 雨, due to its proximity to the verb 降る.)