I think it is a little insincere to say you care to look good only for yourself. I think there is a little defensiveness involved because it seems that this debate gives 2 options - you're either doing it "for you", or you are doing it to attract specfic men. You want to say you're not trying to hook up or get a guy, so you are left with saying you're doing it for yourself.

Realistically, of course it is done for the outside world, but it isn't done with a specific, self-aware purpose in mind. Looking good is socially useful in general, and it gives the attractive person a position of slight power in any environment. Even if they don't plan on doing anything with it, you are aware of it and it feels good because it is potentially useful (this latter part isn't necessarily calculating but a social instinct).

Men are often trying to prove that the woman is lying and she actually has a goal to attract someone specific and get a tangible reaction rather than just an awareness that she could get it if she wanted to.

I think the accurate answer about why looking hot feels good, whom are you trying to look good for is this: Everyone. Every single man outside, every woman, old and young, all people who lay eyes on you. You want "beauty" to be part of your attributes because it is an important attribute to have, and being attractive is in the end a social consensus. You don't need anything specific from your audience aside from that "vote in your favor" so that this status is confirmed again and again.