Here, you can add your CALENDAR from Google Classroom (you'll automatically have one, when you set up your own Classroom). Assignment due dates will be displayed, along with anything else you add to the calendar, such as field trips, assembly dates, parent conferences, etc. You could also just create your own cute calendar as a PDF and post it. The calendar below is a picture of how your Gmail calendar will appear, if you embed it (since I'm not making my calendar public). In actuality, visitors with access could click on your calendar to view events, but they CANNOT edit any of your events.
**IMPORTANT: You'll definitely need to give some thought about how public this information is going to be. Since parents will need access, you'll most likely need to make your site viewable to the public (outside of your domain), which means you might not want your calendar floating around out there. Be mindful of district guidelines and privacy laws**
HOW TO do this: Go to the "insert" tab and scroll down to "Calendar." Then, select the Calendar you'd like to embed on your site. Using "Appointment Slots" in Calendar/Gmail, you can have parents sign up (in real-time) for conference times with you, and they can appear here, if you choose. No need for repeated reminders, since everything is here.