If you prefer a court date for pleading not guilty then you will be assigned to a court of the city you get caught so u gotta travel 250 miles.
Check in ur ticket what the cop used to determine ur speed like radar or followed you. If the cop used radar then it's hard to convince the judge for not guilty but still the judge may reduce or waive the charge (since it's ur first violation though unlikely) based on how u tell the story. Other guys may have idea what to tell...