I have seen here that the expression "to be honest with someone" exists and means telling someone the truth. I also have seen sentences like "be honest to yourself." and "be honest to me." My question is, are both "to be honest to someone" and "to be honest with someone" correct? If so, is there a difference between the two?
"Be honest to me" is not idiomatic. I've certainly never heard it, and it was a surprise to me (native British English speaker) to find any credible search results at all. It appears it is occasionally used, but this ngram shows that it is extremely rare in comparison to "be honest *with".
You may be thinking of examples such as "talk to" versus "talk with", both of which are idiomatic and are sometimes freely interchangeable but with slightly different inferences. You can talk to somebody without them saying much (or anything) back. To talk with somebody infers that you both spoke - you had a conversation.
Although by saying "be honest with me" you are asking someone to speak honestly, honesty itself not a verb like "talk". The verb is "be", and what is idiomatic seems to be driven by how one would show or express the particular quality you are asking someone to be.