I downloaded PayU Integration API php files to be used in EE2, but I am not too sure in which directory to store it? It's not a module or something similar, its just 3 API files I need to reference in my checkout steps. Where would be best to store them in my EE2 project?
I would advise that you built it into an Omnipay gateway.
Omnipay is the payment provider library that powers Exp:resso Store 2 and so by building it for Omnipay it will work on Store.
They have a GitHub with examples and documentation https://github.com/omnipay/omnipay
If you decide to go down that route, the ExpressionEngine Answers website wouldn't be the place to get help. Instead you can use StackOverflow with the tag "omnnipay" and they'll be able to assist there.