Schools in the US typically have summer breaks of about two months, a winter break of about two weeks, a spring break of one week, and often at least a few days for fall break. The dates for those vacations are usually known well in advance of the beginning of each school year. Therefore, schools generally expect you to plan your vacations for those times when school isn't in session, and they aren't usually sympathetic to requests for substantial time off for purely recreational activities. After all, they have to provide substitutes when you're gone, and in most districts, a substitute teacher who can do justice to secondary math instruction is a rare thing.
It is not unusual to have a small allotment of personal days that are intended for unexpected short term situations (my district gives three per year). However, regularly using the entire allotment without a pretty good reason--especially on consecutive days--would be considered less than professional by many administrators.