Hi, Stephanie!
Half-day tickets are not available. You will need to use up one of your days of tickets to enter a theme park. Here is the good news: If you want to add on an extra day to your Magic Your Way ticket, it might not be that much money. While prices are always subject to change, to go from a 5 day to a 6 day ticket is only about $10 (plus tax) so while there is no "half day ticket" this surely is a bargain! Now I do not know how many days you have on your tickets, you can check
HERE to see what an extra day would cost. You can always upgrade your ticket (as long as you do it before the last day is used up). If you purchased your ticket as part of a resort package and want to upgrade before you leave home, call (407)W-DISNEY to upgrade. If you prefer, you can upgrade during your vacation by visiting any Guest Services window in the parks or your Resort Concierge. Just make sure to upgrade before using up your last day of tickets.
If you decide NOT to add on that extra day, use your first day to take dip in the pool, make a dining reservation for Chef Mickey's at the Contemporary, or head to Downtown Disney for some shopping and fun.
However you decide to spend your first day, I hope it is magical!
Let me know if you have any other questions regarding your upcoming Walt Disney World vacation!