Which sentence is correct, and why?
1) It's awesome being by the water.
2) It's awesome to be by the water.
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Both usages are equally correct. In both examples, you are using a verb (being, to be) in place of a noun.
In the first case, you are using the gerund form of the verb, and in the second, you are using the infinitive. The gerund is the more common usage in American English, and is easily identified in most cases by a verb with the -ing ending.
Idomatically, as @user3169 pointed out, being is used more often in the moment, and to be is used more in the abstract. So use being when you are actually standing on the beach, right next to the water, and to be when you are talking about that situation in general.