If you indicate the location, you'd generally use 'There'. For example, 'There's good weather in the south of the country this weekend.' It's possible to use 'it' in a comment with 'weather', though. As a variation on 'It's sunny today' or 'It's cold today', I might say 'It's nice weather today' or perhaps something like 'It's good weather for sailing today.' That said, this could be non-standard or a regional variation, as I seem to remember American members saying that this sounded wrong to them the last time that this question came up.

As an American, I would say "The weather is nice today."

Neither. I would say "the weather is good."