I heard some people talking:
Do you have a favorite beach activity?
If one wrote this, what would seem proper, and, maybe, grammatically perfect:
. . . beach activity
. . . beach-activity
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Compound nouns are common in English:
and possibly tens of thousands more. In fact people frequently make them up as needed:
Come on down to the park this Saturday for our first annual Watermelon Jubilee!
You won't find "watermelon jubilee" in the dictionary, but if you know a watermelon is a kind of fruit, and a jubilee is a big party, then you can assume it's a big party where lots of watermelon will be served.
Only a small percentage of compound nouns are hyphenated, usually if there is any ambiguity about what the noun means. For example:
ice-axe vs ice axe (Both are acceptable, but ice-axe makes it clear that the axe is not made of ice.)
In your sentence, no hyphen is necessary. Beach activity is perfectly natural.