Seeking admission to the USA subjects the returning resident to a whole host of grounds that could result in the returning resident being placed in removal (and subject to detention). Some of the grounds of inadmissibility do not even require a conviction.
An admission to committing a crime, or a suspicion alone of having participated in certain crimes could be enough.
Grounds of Deportability
If you do not travel outside the USA but have a criminal conviction, you may still be eligible for citizenship or at the very least not deportable.
However, when you take that cruise or go home to visit family you could return to your worst nightmare. This is because you become subject to the grounds of inadmissibility which are more expansive.
If you are not sure, I recommend you don't take any chances.
Additional resources provided by the author
Immigration and Nationality Act Section 212(a) for grounds of inadmissibility and Section 237 for grounds of deportabilty.