The best time I find is sometime in June and here's why:
1) You can submit your AMCAS June 1 or 2nd and have it verified but it won't be sent to medical schools until the first batch is transmitted sometime in mid to late june. This year was around June 15 or 17th I think. So there's a period of about 2 weeks where you literally have nothing to do.
2) Most medical school secondaries don't become available until late June or early July anyway, shortly after the first batch of primaries are transmitted
3) Applications probably won't get reviewed until mid-July at most places
4) Because of #3, the earliest you can usually expect interview invites will probably be mid-late July with the actual interviews starting mid-late august.
So if you submit your AMCAS super early (in the first week or so), I'd go travel immediately after that in June, you'll have at least a 2 week window. If you submit a bit later (mid June onwards), the delay for verification (and hence most secondaries) will be anywhere from 2-4 weeks which is the window I'd aim for. Finally, you could also go during May when you can't submit your application. But you probably will want that time to focus on editing your essays and putting the finishing touches on your application.