Welcome back to the Disney Parks Moms Panel, Amy!
This is a great question! Strategizing to enjoy attractions while avoiding the parade route and guest traffic is something I have done several times, so I am happy to offer you my advice.
There are two parade events that occur at varying times during the day that may interfere with your ability to get around:
Move It! Shake It! Dance and Play It! Street Party - This fun dance party is offered three times a day, so crowd levels stay pretty low, and will only affect Main Street USA and the Castle Hub Area near Cinderella Castle. Select the highlighted link to check showtimes for the day of your visit, and to view an interactive map that includes the route.
Disney Festival of Fantasy Parade - This headlining 2:00pm parade steps-off near Splash Mountain between Adventureland and Frontierland, continues through to Liberty Square, circles around the Castle Hub and then heads down Main Street USA for its magical finish. This is definitely the parade you'll want to strategize around.
Amy, to maximize your experience while the parade is in session, I highly recommend staying in the Tomorrowland and Fantasyland areas - this puts you on the opposite side of the parade route! Another great tip is to download the My Disney Experience Mobile App for your smartphone. The app will allow you to check wait times, parade times, and includes the same interactive map available on the website, allowing you to further maximize your touring strategy.
I hope this information helps you plan a pixie-dusted day, Amy. Please let me know if you should have any additional questions.
Have a fantastical time!
Faith