Hi Amy,
Thanks for your question as I'm sure other guests are curious, too, about St. Patrick's Day celebrations. Traditionally, Raglan Road is the place to be for all St. Patrick's Day festivities. The Disney Parks Blog offers an entire line up of activities beginning tomorrow through the holiday, and by searching "St. Patrick's Day" you'll also find commemorative merchandise offered in the Disney Parks, like t-shirts, hats, Duffy the Disney Bear and Disney Pins to help celebrate the Irish!
You won't find St. Patrick's Day to be celebrated much in the Parks in terms of parades or events, however I'd suggest booking an Advanced Dining Reservation at
Rose & Crown Pub & Dining Room as I'm sure the UK Pavilion in Epcot will be bustling with Irish excitement! Continue to check daily as reservations might open up due to cancellations.
Have a wonderful time, Amy!
Slainte!