Hi Nate,
There is not currently an out-of-the-box way to display events without an exact date. Sorry for the bad news there!
You could however do a customization to change the way the event displays. If you’d like to give it a shot, our themer’s guide is the place to start! We are not able to provide technical support here in the Pre-Sales Forum, so if you need further assistance with this, will you please post this question in our Events Calendar PRO forum? We use the Pre-Sales forum to answer questions about the features of our premium plugins for those interested in purchasing them. However, please note that even there, we are limited in the amount of support that we can provide for customizations.
If you have not purchased one of our premium plugins, you can post in our community forum on wordpress.org, which we review weekly to check for bug reports. If you need more in-depth support, you will need to purchase a license.
Our knowledgebase is a great place to start looking for answers. You can also search our premium forums to see if another user has posted about a similar issue.
Thanks,
Jennifer