The word "there" in this sentence doesn't seem to be necessary. But if it is there, what exactly is it? A noun? An adverb?
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Yes, 'there' can be used as a noun (or arguably a pronoun) to refer to a location as a subject or object.
There is still a noun, and the direct object, in this sentence. The way you tell is, you can insert a comma:
This is still correct, so "See there" must be the main clause of the sentence; where is acting as a subordinating conjunction rather than an adverb, and it's fine in English to use a subordinate clause to modify the direct object. A further check is to delete the clause:
Telegraphic perhaps, definitely requires context to make sense, but still a valid sentence.
Addendum: You can't say
because there requires where in this context. It is the same phenomenon as not being able to use which or that to refer to people:
Soapbox: This seems to be yet another situation where schoolbook grammars mislead by trying to bend English to fit an analytic paradigm designed for Latin. Most words in English can play the role of at least two parts of speech (for instance, as a wise man once said, [nearly] all nouns can be verbed). In particular it might be analytically cleaner to merge the categories "adjective" and "adverb" and reconstrue the -ly suffix as an agreement marker rather than a derivation operator.