For this weekend, I hope to go to the sea. In the state where I live, autumn is beginning.
In my opinion, it is the best season - the climate is good and there are few people at the beach. The water will be little bit cold, but I have bought a wetsuit so I will be able to go swimming.
*You're going to the sea for the weekend, so the correct preposition to start with is 'For'.
*Verbs go after the noun they are describing, so we would say 'autumn is beginning' (you could use 'starting', 'beginning' sounds more appropriate for this when writing).
*People are AT the beach, it is a location/place where they visit. Saying people are 'in' the beach would infer something like everyone being underneath the sand or something silly like that!
*I've taken out your 'today's, because the prompt is asking about future plans, and you started it off that way by saying what you plan to do for the weekend.
*I get the tense you're trying to convey with 'will can', but the grammatically correct way to write that is 'will be able to'