About an offering to Athena

Would it be appropriate to offer Athena a drawing or painting I have made?

Do you mean offer, or dedicate?

An offering is something given up to God, whereas a dedication is something like a tribute of respect. Fine sculptures and other architectural works would be dedicated to certain deities and installed in the sanctuaries.

Small votive statues (usually of lightly-fired terracotta, but occasionally of bronze for those wealthy enough to afford them), as well as votive plaques and symbolic tokens called tamata, however, were also common as offerings, their level of artistry usually (though not always) being relatively simple, because they were not meant to be enjoyed as decorations, but instead, offered up to the deity.

Temples of Asclepius were particularly known for people commonly offering votive statues and tokens, and frequented temples would fill up with them rather quickly. When this happened, they would be gathered up, usually smashed or crushed, and then buried nearby, often within the temple grounds, because they had been offered to the deity, and no longer belonged to mortals.

If you want to offer your painting, that is acceptable, but you need to be aware that, if you do so, it no longer belongs to you. It is not a decoration, and you also have no right to take it back.