TL;DR The subject of the sentence is indeed the preposition phrase over there.
We normally expect the subjects of sentences to be noun phrases or sometimes clauses. However, they can occasionally be adjective phrases, preposition phrases or even adverb phrases.
Preposition phrases can be the subjects of clauses using specifying, but not ascriptive BE. In the Original Poster's example, BE is being used in its specifying and not ascriptive sense and therefore this preposition phrase is contender for subject of the sentence.
Preposition phrases do sometimes appear as complements at the beginning of clauses which display subject complement inversion—where they are not subjects. However, this usually occurs when the locative phrase occurs with the verb BE used in its ascriptive sense:
Over there are some tweezers.
Here the subject of the clause is some tweezers, and the preposition phrase over there is giving us some information about the location of these tweezers. Notice that the verb BE agrees with tweezers here, and not the preposition phrase over there. However, this is different from the OP's sentence where the verb BE has an equative meaning, and the sentence could be modelled as:
Over there = where I'll be.
Notice that we cannot do this with the other example:
Over there = some tweezers.
These facts would seem to rule out the Original Poster's example being a case of subject complement inversion. It is possible for us to have subject dependent inversion with specifying BE, but only in very flowery poetic type environments, very different from the Original Poster's example:
The king of the meadows am I.
There is no indication that any other phrase has inverted with the phrase over there in this sentence therefore.
The phrase over there, then, is in the canonical subject position, occurring before the verb, and we have good reason to believe it to be th subject.
We could do the subject auxiliary inversion test to double check if over there is the subject. If we turn the sentence into a question, the subject should invert with the auxiliary BE:
Is over there where I'll be?
Here we see the phrase over there has inverted with the verb is giving further evidence that it is the subject.
Lastly, outside of imperative constructions, all well-formed English sentences must include a subject and a predicate. By reducing the sentence using pro-forms to substitute in for these two parts of the clause, we can tell which bit of the original sentence is the subject, by seeing what the subject pronoun is standing in for:
Over there is where I'll be.
In the second sentence above the word it appears to be standing in for the preposition phrase over there. The verb is is standing in for is where I'll be. Because the subject it has replaced the subject of the original clause, we can see that the subject of the original clause is over there.
In short, all of the evidence points to the preposition phrase over there being the subject of the example sentence.