Is directly showing a characters inner thoughts and conversations with themselves too telly or cheesy?
Not necessarily, but the propensity to indulge in internal monologue is itself a character trait. Fundamentally, the way we assess the character of someone in fiction is the same a how we assess their character in life: by their actions. Sometimes it makes sense to shortcut the process of establishing character by telling us directly some aspect of the character's character, but even that is best done by telling us how the typically act (as opposed to dramatizing a whole scene).
So, if you show a character's internal monologue, readers will interpret that first and foremost as a piece of behavior and will judge first and foremost that indulging in internal monologue is a character trait of the person.
Will the content of that internal monologue also reveal aspects of their character? Sure. But you have to treat that in context of the broader effect of showing all that internal monologue. If you use it to reveal a character who is not contemplative by nature, the dissonance will be obvious and will undermine what you are trying to achieve.
Inner monologue is used quite frequently, and it can reveal character traits that may not be revealed any other way: True feelings.
Such as, if Jack is telling the truth about never cheating on Jill, if the photograph of him doing so had to be faked.
The same with secret desires, dislikes, hatreds, plotting, faking friendship or even faking love or sexual attraction for nefarious purpose. Jack may have faked his love for Jill to get laid. Or alternatively, Jill may have faked her enthusiasm for Jack's clumsy and laughably stupid seduction of her, to become trusted enough by him to rob him blind.
You should not abuse inner thoughts, readers trust they are the real thing. Just like in real life, actions and dialogue can be misleading lies. Inner dialogue should be the true thoughts; I think it would be a violation of the "reader contract" to find out they were lied to by some previous passage portrayed as an inner thought or feeling.
It's not inherently bad
It is a trap where too many things as resolved through inner monologue when it might make the story more dynamic. I suffer from that big time where the character thinks and thinks and thinks about stuff but does not do anything about it. My personal take is that it is not bad, but whenever you can have the character DO something that would prove the dialogue, it helps.
Keep it short whenever possible. Show, don't tell. And thinking about stuff has a bad tendency to have you tell, rather than show.
Inner monologue can be used to GREAT effect. As others have said before me, it isn’t inherently bad or cheesy. Depending on the medium however, should determine how often it is used. If Your Project Is A:
Visual Novel: Inner monologue is practically essential, however if you can see the character than you should have their monologues supported by character animation.
Book: Inner monologue should be used specifically with the protagonists opinions about other characters and the situation at hand. However remember the rule of “show don’t tell,” especially in bigger, pivitol moments your characters actions should indicate your character’s feelings, as actions speak louder than words.
Film: I would use this very rarely. Voice overs are used sparingly in film for a reason. As you can both see and hear the emotions of a character, “actions speak louder than words” and in film this is a must. I would only use it if you deem absolutely necessary, for perhaps the tone you want.
Something Else: Try to think of the most notable example of inner monologue in that medium you can think of. Figure out how effective you think it was, and why it was effective, and use that as your baseline. If you can’t think of any, then there is likely a better way of doing it.