for
（表示對象、用途等）給，對，供?
used to show who is intended to have or use sth or where sth is intended to be put
There's a letter for you.有妳壹封信。
It's a book for children.這是本兒童讀物。
We got a new table for the dining room.我們給飯廳添了壹張新桌子。
This is the place for me (= I like it very much) .這裏很適合我。
Of
屬於（某物）；（某事）部分的；關於（某物）?
belonging to sth; being part of sth; relating to sth
the lid of the box. 盒子蓋
the director of the company. 公司的董事
a member of the team. 壹名隊員
the result of the debate. 辯論的結果
摘自牛津詞典
由此不難看出，of更多表示所屬關系，而for是功能上的“為、給、關於”；所以當妳說forecast of tomorrow的時候更多表示“明天(新聞上播出的，預報內容和明天關系不大，只是表示播出時間是明天)天氣預報”；而forecast of tomorrow則是“對明天的天氣預報”。
E.g. The forecast of yesterday for yesterday is wrong; It didn't rain at all yesterday! 昨天預報的昨天天氣不準，昨天根本沒有下雨！