In The Importance of Being Earnest, honesty is certainly hard to extrapolate as a character trait in any of the major players. Just when we think someone is coming out redeemed, speaking the truth, or showing true emotion, we are slammed with an epigram, or a paradoxical statement, that directly contradicts what the character says or does.
Now, if honesty is to be compared between Jack, Algernon, Gwendolen, Cecily, Lady Bracknell, Prism, Chasuble, and the two waiters it would be best to base the final answer more on what the characters actually do than on what the characters say. This leaves out Chasuble (who is a very strong candidate), and Lane as well as the other butler. We do not know enough about them to make an informed decision.
If, in contrast, we turn to the two most important characters, Jack and Algie, we find that, although they both are honest with each other, they weren't always so. Jack did not know about Bunbury and Algy did not know about his friend Ernest's name being actually Jack. So, they were not always honest to each other. Moreover, they are not honest to their families either, as they assiduously keep their secret lives quite well-protected.
As far as the women, Prism lives hiding the secret of where she came from and what happened to her at the cloak room of Victoria Station (the Brighton Line). She definitely is not completely honest about who she is, nor is she openly honest to Dr. Chasuble about her emotions; not that she could, anyway, it would have been improper of a lady.
Gwendolen and Cecily are very hard to identify as honest because none of them has explained the true reason why they want a man named "Ernest" for a husband, just for the sake of the name. The shallow superficiality of the women, the speed with which they fall in love and the lack of solid foundations in their behaviors and choices make them ill-examples of honest women.
This leads us to, perhaps, the only honest person in the play: Lady Bracknell. Although brash, abrasive, and snobbish to the core, Lady Bracknell is quite honest in the way that she expresses herself.
Lady Bracknell does not hide her disdain for sick people,
I think it is high time that Mr. Bunbury made up his mind whether he was going to live or to die. This shilly-shallying with the question is absurd. Nor do I in any way approve of the modern sympathy with invalids. I consider it morbid.
and she certainly does not even try to pretend to be kind to Jack Worthing, whom she considers as a nobody for not having any connections known to any great family. She even disregards the fact that he is an orphan,
To lose one parent, Mr. Worthing, may be regarded as a misfortune; to lose both looks like carelessness.
insults his background, and demands that he finds out who his parents are before she decides whether to consent to a marriage or not.
I would strongly advise you, Mr. Worthing, to try and acquire some relations as soon as possible, and to ...produce at any rate one parent, of either sex, before the season is quite over.
Her expressions are mean and insulting, but she belongs to a higher social sphere that has historically demanded special treatment and the best of everything. Hence, she is quite real and honest in being herself. She also demands the truth in others. It was she who recognized Prism and made her confess to what happened at the cloakroom. In the end, Lady Bracknell is merely a product of her time...but indeed an honest one at that!