An example question is say if I hashed inserting string "Hi" to 3 and there were no peers at 3 it would go to the next available peer and store it there right? Or where does it store it's values to?
I already answered a similar question for bittorrent/kademlia, so just to summarize in a more general sense:
DHTs store the values with some redundancy on N nodes whose ID is closest to the target hash.
Considering the vastness of >= 128bit keyspaces it would be extremely unlikely for nodes to exactly match the key. At least in routing schemes where nodes don't adjust their IDs based on content, and chord is one of those.
It's pretty much the same as regular hash tables, hence distributed hash table. You have a limited set of buckets into which the entries are hashed, where the bucket space is much smaller than the potential input keyspace and thus does not precisely match the keys either.