Where's Central park? - Good. What's the address of Central park? - Good. What's the Central park's address? - No need for the word "the" here, because we're referring to specifically named location (Central Park) and thus don't need "the" to further specify it. I would also capitalize "Park" in these sentences since "Central Park" is the full, proper title of the location.

I agree with Holly about locations in general, but the location of a park is not usually referred to as its "address." You can't reply to these questions by giving a specific address (for example, "Central Park is at Number 5 Park Avenue.") Instead, to answer these questions you would describe the streets that border the park, or give an intersection where a person can enter the park easily. You may want to ask "Where is Central Park located?"