It doesn't matter if you're a man or a woman, straight or gay, if you're having sex outside of a long-term, mutually-monogamous, relationship where both partners have been screened for STDs, it's probably a good idea to practice safe sex. In most cases, that means that someone has to buy condoms, even if it's only to cut them up and make them into dental dams.
There seems to be a highly prevalent sex myth that, in heterosexual couples, it is the man's responsibility to buy condoms. Although there are good reasons why some men might prefer to buy their own condoms - such as having a favorite condom brand - it's actually good idea for anyone who is considering having sex to buy condoms.
One reason that everyone should buy their own condoms is that it's always a good idea to be prepared if you're thinking about having sex - because your partner might not be. If you assume that they're going to buy condoms and then they don't, you could be faced with a very unfortunate choice - having unprotected sex that you may end up regretting or not having sex at all.
Some women may be reluctant to buy condoms because there is also a sex myth that a woman who carries a condom is a "slut" or a "tramp." Although there are a small subset of men who believe this, you may want to question whether you actually want to sleep with someone who judges you for conscientiously choosing to have sex with them. Deciding to have sex should be something that you do from a place of personal empowerment, which includes having the ability to take care of yourself both emotionally and physically. Anyone who doesn't respect that may not respect you either.
Simply put, it is not the responsibility of the man to buy condoms. It is the responsibility of anyone who is planning to have sex to be prepared to protect themselves and their partners. If one partner has a strong preference for a condom brand, or needs a special brand of condoms to deal with a latex or lubricant allergy, then they may take on the major burden of condom purchasing, but there's no reason why the other partner can't chip in or keep a few backups in the nightstand.
Finally, for the women who don't want to buy condoms because they're afraid of "how it will look," it's worth mentioning that several companies are now making fashion-forward condom cases... just in case appearances are more important than taking care of your health. And, of course, you can order them online.