Person 2 is being dreadfully picky in my opinion. For one, to say that something "sounds very ghetto" as a negative is pretty insulting to anyone who lives in a ghetto. There are certain racial and social undercurrents to this statement that are far too complex to go into here as well. To get an idea for yourself, google "ghetto speech" and you will see a wide range of interesting material, as well as a good deal of hateful and racist commentary.
Suffice it to say that "where is it at?" as opposed to "where is it?" is somewhat "slangy" but also commonly used, at least in American English. Whether or not it is technically grammatically incorrect, it is common enough that most people just don't care.
Also, the informal idiom where it's at generally means a fashionable place where the most interesting things are happening at present. By extension, it can be used to refer to people, things or activities as well:
Studio 54 is where it's at.
Whole wheat spaghetti is where it's at.
Kant's Critique of Pure Reason is where it's at.
And so on.
SUPPLEMENTAL to Maciej Stachowski's ANSWER
Cool as Slang
This use of cool appears to have arisen among urban African-Americans in the 1930s. It was widely adopted among admirers of cutting-edge jazz (the 'beats') shortly after WWII, and spread in the 1950s into the speech by which young people (those in their teens and early twenties) distinguish themselves from their elders—which is what we usually mean by the term 'slang'.
Cool was virtually universal in my generation, the Boomer cohort. It has remained in use among us, and has been received into the speech of succeeding generations: I hear it a score of times a day in my shop and from my Millenial son and his friends.
If you come to the U.S. you will find many, many elderly people—me, for instance—employing cool as a universal approbative.
So I think cool in this sense has long since passed out of 'slang' and become an ordinary mainstream colloquial usage. Indeed, I think we can pin down just when this happened: in the mid-80s, when the surfer speech community started preposing their fresh slang intensive way. Clearly, cool was no longer sufficiently marked to represent the language of an in-group. By 1990 the chat-room l33t found it necessary to invent a new spelling, kewl, to indicate that their use of cool was ironic.
Best Answer
Actually I would argue that 'whatever' is synonymous with "I don't care". However, there are certain circumstances when "I don't care" is used.
Here are some that I can think of:
Getting into an argument about something, and brushing the accident off with 'whatever'. Note: This may not be the best way to use 'whatever' to look cool, because it is somewhat rude and dismissive as @ColleenV mentioned (dismissive: feeling or showing that something is unworthy of consideration).
(meaning I don't care to argue about this anymore)
Losing your train of thought — where you are talking about something but completely forget what point you are trying to make.