DR/Reporting solution for a large SQL Server database We have a large (3TB) database that is a part of AOG. We now have a need for a third copy of the data. Here are some of things we need: 


The third copy needs to be in sync with the primary in real time (or near real time); worst case we can live with a 24 hour lag. 
The third copy cannot be PRIMARY NODE any time. (This is just a reporting server)


What are my options? 

I don’t want to configure replication on top of AOG. That seems like a complex option. I can add a third node for the AOG. This could add some dependency on the primary; I’d prefer the new architecture to minimally interfere with the other 2 nodes.
If you don't need to query the server, the classic answer here is transaction log shipping: simply restoring your backups on a different SQL Server.

It's a great fit here because:


It's independent of your Always On Availability Group: even if the AG fails or the cluster fails, you can go live with this DR server quickly
It can't become the primary node until you manually run RESTORE WITH RECOVERY and point your clients over to it (can be tuned by using a DNS CNAME that normally points to your primary, but during disaster, you change it to point to the log shipped secondary)
It can stay reasonably in sync - you said within 24 hours, and that's fairly easy to do with log shipping


That meets all  of the requirements in your question. 

Just be aware that there is a licensing gotcha: if you have Software Assurance, then for every one primary you buy, you get one free secondary as long as it's not queried. If you're using multiple secondaries (like one in your primary data center, plus adding this new one,) you may need to purchase additional licensing.

If you DO need to query the server while it continues to update the data underneath you, your only two answers are Always On Availability Groups or transactional replication. All other answers (SAN replication, log shipping, VM replication, etc) will require queries to stop each time the data is updated.