I've never played a drow personally, but if I did I'd just ask myself the same question of that character that I ask of all my characters...
"What do I want?"
That's it. What is motivating me to travel with this small band of people and doing stuff? I must be doing it for a reason. And so long as what I want can be accomplished while traveling with this band, then there's no reason not to do so and to work around whatever roadblocks get in my way. Once I figure that out why my character is doing what it is doing and if/how his traveling partners can facilitate it... everything else is gravy.
And as far as the "drow are evil" thing... that is such a minor sticking point. There are millions of personality quirks that can be designated as "evil" that never once impact your place in the group, nor cause much issue for them at all (presuming I select a quirk that is not directly in opposition to any other character.) Maybe my character finds animals to be as inconsequential as insects and thinks nothing of killing them like others do of swatting a mosquito. So long as I'm not in the same party as a Beastmaster Ranger, my "evilness" will rarely ever come up or cause issue. Or perhaps I just find my own personal happiness is more important than anyone else's, and thus have no problem taking what I want from those who won't even realize it's gone or I won't ever see again. And no, that doesn't mean I'm going to steal from my own party members, because part of my happiness is dependant on their happiness too. If traveling with them is important to me in getting what I want, I'm not going to deliberately do things to make them upset. But thinking nothing of grabbing an apple off a cart as I walk by? Absolutely I can do that.
I think way too often players just think that to play evil characters they have to behave like these massively huge, maniacal archvillians, where every action they take just screams "I'm evil! I'm evil! I'm evil!" to the entire world. And that isn't true at all. You can be "evil" simply by just not caring about the well-being of most other people. And it never needs to come up, it never needs to be "a thing" in the game, it never even needs to be known by the others at the table. So long as your character just strives to get what they want (and that want isn't in direct opposition to the wants and needs of the others in the group)... you can have the standard "drow are evil" trope but never once have it matter.