NPs - pre-/postmodifiers
In a comment, BillJ wrote:
"Both" is a predeterminer in NP structure, e.g. "both the children". But your example is a correlative coordination construction where "both" is paired with "and". Here, "both" is a determinative functioning as a marker of the first coordinate: "The swimming pool is [both a great place to relax and a perfect spot to do some exercise]."