Hey Jason,
Thanks for reaching out! Glad to hear you’re looking into our plugins. 🙂
Yes, I do believe that The Events Calendar will do exactly what you’re looking for here. Even in the free version, you are able to create as many venues as you would like and associate those venues with any number of events. The plugin performs very well in and of itself, though, I would say that if you are publishing a huge number of events (in the thousands), then you may want to look into a dedicated server option for hosting. I would make that recommendation for any WordPress site, even with default Posts.
If you would like to have Venue and Organizer pages and other features, like recurring events and additional calendar views, then that where I would suggest looking into our Events Calendar PRO add-on, which extends The Events Calendar with those and more features.
Does this help answer your question? Please let me know. 🙂
Cheers!
Geoff