I would like to play tennis today
I like to play tennis today
Would you tell me which one you would rather use?
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I would like to play tennis today.
Would like indicates that you're talking about a possibility that may or may not happen, and you're expressing your desire. That's appropriate for talking about a specific time frame, like today. The word would other parallels other constructions that describe a consequence of a hypothetical condition, like “If it is convenient to play tennis today, then I would like to.”
When you say “I like to…”, you are describing your desires or your personality in general, not in relation to a specific time frame and not as a consequence of some hypothetical condition. It’s ungrammatical to say “today” here, because stating a specific time frame conflicts with the timeless meaning of “I like to…”