for
（表示对象、用途等）给，对，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.有你一封信。
It's a book for children.这是本儿童读物。
We got a new table for the dining room.我们给饭厅添了一张新桌子。
This is the place for me (= I like it very much) .这里很适合我。
Of
属于（某物）；（某事）部分的；关于（某物）?
belonging to sth; being part of sth; relating to sth
the lid of the box. 盒子盖
the director of the company. 公司的董事
a member of the team. 一名队员
the result of the debate. 辩论的结果
摘自牛津词典
由此不难看出，of更多表示所属关系，而for是功能上的“为、给、关于”；所以当你说forecast of tomorrow的时候更多表示“明天(新闻上播出的，预报内容和明天关系不大，只是表示播出时间是明天)天气预报”；而forecast of tomorrow则是“对明天的天气预报”。
E.g. The forecast of yesterday for yesterday is wrong; It didn't rain at all yesterday! 昨天预报的昨天天气不准，昨天根本没有下雨！