"A bar would be so cliche and expected.  And if someone saw us at 7-Eleven, it's not like they could assume we were conspiring or having sex or anything.  It would just be 'Wow, is that that girl and that guy whose ass she beat?  Huh, what a weird coincidence!'  And if they come in and ask what's going on, you can make a witty rejoinder about my needing to buy more ice for my face."