I've been waiting for some native speaker to give you an answer. Here goes mine. The omission of "where" in this relative sentence doesn't sound ok to me. Too informal but maybe correct.
You can never omit "where" when a referent noun doesn't appear before. "This is WHERE I was born." "where" cannot obviously be omitted here.
I agree that "This is where I was born" sounds the most natural. As hellx also mentioned, "This is the place I was born" is colloquial, but not grammatical, since you're not born as a place, but born in a place. To see what I mean, consider the equivalent sentence: "This is the place that I was born." This is similar to the common expression, "The place to be" (which literally means "you should be that a place" but understood to mean "you should be in/at that place").
For this reason, "This is the place I was born in" actually sounds better to me, since it is the common way of saying, "This is the place in which I was born" – where "in which" is a precise substitute for "where". Of course, remember that the dangling preposition "in" is controversial.
My two cents...
The best one grammatically is: This is the place where I was born.
This uses two clauses, "where I was born" is the subordinate clause.
If you omit "where" you have an imcomplete clause.
Also, It is best to not end a sentence with "in"
Thank you everybody. It is well explained in every post, but I haven't got it clear yet. Can I omit WHERE in relative clauses?
Sorry for this insistence but I'm a bit stuborn when I don't have things clear...
Yes, in this particular sentence "where" may be omitted, but similar instances are rare and frequently sound unnatural.
In your example, "where" is not functioning as an adverb or as a subordinating conjunction, but as a relative pronoun, often called a "relative adverb." When used as relatives, the adverbs "why" [the reason (why) he left] and "when" [the year (when) Kennedy was assassinated] also fall under this category.
To be safely elided, a relative pronoun must meet two requirements:
1) The relative pronoun cannot be functioning as the subject of the verb within the adjective clause, e.g. "She met a guywho works downtown."
2) The omission must leave the meaning of the sentence intact.
The relative "where" will always meet the first requirement, but only now and then the second:
"This is the exact spot I last saw her."
Although on stylistic grounds the sentence above may be argued, grammatically it’s sound.
Relative clauses are very different, but the construction in English is very similar to that of Spanish. For an overview of these, please go to the link listed below.
The short answer to your question is in colloquial speech, English speakers might leave out relative pronouns/adverbs, but this omission could be very confusing when done with "where." But for accurate grammar, you should include them.
"That is the building I work" (incorrect)
"That is the building where I work" (correct)
An excellent grammar site, link for relative clauses is called chompchomp
Sorry, I guess I can't post URLs at this time.
"This is the place I was born." This is common way of speaking, you will hear it all the time.
Also "This is the place they shot John Lennon", "This is the place I crashed my car", "This is place I was sitting when I watched Tom Brady's knee get ripped to pieces", etc., all sound pretty good to me. The problem is that I soon as a replace the word "place" with some other reference to a location in space, it sounds really bad, i.e., wrong.
"This is the city I was born." No way. Need the "where" or equivalent.
"This is the house I was born." Uh-uh. Nope. Also needs the relative pronoun.
"This is the intersection I crashed my car." No good.
Why does it only sound good with "place"? Does this have more to do with how we use that word than anything else? Because I can tell you that "This is the place I was born" is a very common way of saying this, not rare at all.