I will comment on the two sentences you wrote, then I will suggest the more common way to say the same thing. "It's good weather today" - English speakers almost never say it this way. "it's a good weather today" - this is not proper English as Brad explained (no "a") The weather is good today. Today the weather is good. Dark Panther's sentence is also correct.

"It's good weather today." We never use "a" with "weather" unless we are referring to "a weather emergency" or some other example where "weather" is an adjective.

What fine weather we have today!

"The weather is good today." The native way to express this: "It's a nice day today." (the implied meaning is that the weather is pleasant)

In your original question, "weather" a noun; in my answer, I said that you could use the articles a/an/the if you turned "weather" into an adjective. So yes, we can also use articles before other adjectives like "good."