There is no standard "school holidays" in the US, as in England for example, where ALL public schools are on break at the same time. (FYI, the British spring holidays this year are from April 2-April 18th.)
Spring break can usually be anywhere from mid-March to late April, so if you really don't want to risk encountering Spring Breakers at all, skip March and April altogether. However, if you are just looking to skip the very worst of it, avoiding the week preceding and the week following Easter should be sufficient.