पर can also mean "at", in the sense that you are "at home", "at the beach", "at the store", etc.
If somebody directed you to go over to the table, you could walk over to the table and say मैं मेज़ पर हूँ to indicate that you have arrived at the table, but out of context there is ambiguity between "I am on the table" and "I am at the table".
If you really wanted to be unambiguous, I think you could say मैं मेज़ के शीर्ष पर हूँ to mean "I am on top of the table" (lit. I am on/at the table's top), or मैं मेज़ के बगल पर हूँ to mean "I am next to the table" (lit. I am on/at the table's side). But that's a little too complicated for this point in the course...