I have a significant other living outside the US and I want to visit them every 3 or 4 months. Currently, I am a permanent resident of the US. Is it okay if I travel abroad every 3 or 4 months and stay outside of the US for about 1 week each time?
Of course it's okay. There are some consequences to remaining outside the United States.
if you stay out for longer than 180 days then the immigration officer should examine you as an "applicant for admission" when you return, potentially exposing you to greater risk of being found to have abandoned your residence in the United States (although the risk remains very low). One week is much shorter than 180 days.
if you stay out for one year or longer then your green card is not valid for entry to the US (but it remains valid for other purposes). One week is much shorter than one year.
if you fail to maintain sufficient continuous residence in the United States you will not qualify to naturalize. One week is too short an absence to constitute an interruption of your residence in the United States.
If you're worried about these trips for some other reason, please let me know in a comment.