Hello Cecilia!
Welcome to planDisney!
Early Theme Park Entry is a privilege for guests staying at Walt Disney World Resort Hotels that lets them enter the four main theme parks 30 minutes before everyone else. When I am motivated with vacation energy this is one of the best times to enjoy at least a few attractions with very minimal wait.
Now, you stated that you don't have early theme park entry so your mornings will look a bit different but it can still be fun. Lucky for you, the restrooms or bathrooms are located outside of the Park entrances for all four main theme parks so you do not need to use a ticket or worry about Early Theme Park Entry. You can locate them easily using the map feature in the
My Disney Experience Mobile App and typing in "restrooms". I found that
Magic Kingdom Park and
Disney's Animal Kingdom Park restrooms are located to the right as you approach the gates. At
EPCOT and
Disney's Hollywood Studios look to the left for the restrooms. These are traditional restrooms or bathrooms and have toilets with handwashing sinks and diaper-changing stations. I don't know if you are expecting showers but they won't have those.
All of the lockers for the four theme parks are located just within the Park entrance areas after tickets are scanned. For some of the Parks, this works out fine as all guests can be allowed in up to a point while guests with Early Theme Park Entry have a scan point where they can go further in to enjoy the open attractions. This is most evident in Magic Kingdom Park, Disney's Animal Kingdom Theme Park, and EPCOT but in Disney's Hollywood Studios guests without Early Theme Park Entry could be held outside of Park entrances until it is time. This could change at any time based on Park capacity and decisions made by the "powers that be."
So getting to that locker may be dependent on the Park and the day you can go. This may be also true for the shops as the hold point for non-Resort guests varies by the Park. In Magic Kingdom Park, EPCOT, and Disney's Animal Kingdom Theme Park you may make it to the shops due to how it has been lately while Disney's Hollywood Studios, may not be accessible.
I suggest you prepare yourself to be able to access the restrooms and
potentially the lockers and shops when entering the parks during the Early Theme Park Entry time as a non-Resort guest. Use your My Disney Experience Mobile App mapping feature to guide you to where you want to go so you can be efficient with every minute in the Parks.
I hope this helps and you have a lovely time!
Happy Planning!
-Nimmy