rent

[loveydovey]

Which is correct? " I am looking for an apartment for rent or I am looking for a rent in your building?"

[Ravage]

Of the two "I am looking for an apartment for rent." is the better choice.
You could change the second one to "I am looking to rent an apartment in your building." and it would be acceptable that way also.

[Anglika]

There is also a usage: I am looking for a rental in your building.