Me and my friend got into a debate

Can you end a sentence with the word at? eg: Where do you work at?, Where did you buy the shirt at?

[Tdol]

There's no need to do so in those examples, but you can do it:
Which point did you leave at? (less formal)
At which point did you leave? (more formal)

[Mister Micawber]

.
In fact, sometimes it is all but mandatory:

What are you looking at?
.