he correct sentence is:
"It's going to rain tomorrow."
Explanation:
"It's going to rain tomorrow."
"It's" is a contraction of "It is," which is appropriately used here to refer to the weather.
This sentence clearly and correctly conveys the prediction about rain.
"There's going to rain tomorrow."
"There's" is a contraction of "There is," which doesn't fit well in this context.
A correct alternative using "there" would be: "There is going to be rain tomorrow."
"There will rain tomorrow."
While grammatically possible, this sentence is awkward and not commonly used.
A more natural phrasing would be: "It will rain tomorrow."
Summary:
"It's going to rain tomorrow." is the most natural and grammatically correct way to express the forecast.