Dear Rabbi Simon
Can one go to an amusement park on shabbat if they already paid for the ticket and are walking back and forth to the park?
As a matter of principle, it is difficult to approve of attending an amusement park on Shabbat, as doing so is not in the keeping of the spirit of the day. There are of course considerations of electronic circuitry or similar, which may involve actual Shabbat infractions. Carrying a ticket presents a problem (unless the area is within an eruv). The ticket itself may also be muktzeh.
Strictly speaking, however, to enjoy the atmosphere, company of friends, exhibits, performances, shows, music, etc, would not involve Shabbat violations per se. Any more specific guidance would be dependent on a fuller understanding of the particulars of your enquiry.
I hope this is helpful.
Rabbi Rashi Simon