I feel that there is a higher chance for me to produce publications if I stay with my current advisor
One of the very best outcomes of a postdoc is publications. Academia is essentially built on publish or perish. All other things being equal, I would go where your chances of publication are the highest.
I would also explore options for collaborating with the PI overseeing the potential postdoc in the nearby city. Is there still an opportunity to broaden your network by doing some collaboration? Just a thought.
I have evaluated a few job candidates who have a postdoc. (I work in industry, not academia). I usually do not care where they did their postdoc. I care what they did. Generally speaking, I would much rather take a candidate with three publications with their old PhD advisor than someone with one publication at an institution different than their PhD granting institution.*
One thing I will mention is the benefit of opening an entire new network of opportunities by going to a new institution for a postdoc. At my former PhD institution (call it U of X), most PhD grads end up in some low level academia position (community college, non-research teaching university, etc.) Networking was really tough at this university.
At U of X, I shared an office with a lady who had an opportunity to do a postdoc at U of X. She had published several papers with her advisor already and likely would have published many more. However, U of X has mediocre to poor faculty networking (a discussion for a different day. Long story short, when a department hires a bunch of their own PhDs as professors, it's not good for networking). She decided to leave to another institution for a postdoc. She only published one paper during her postdoc, it just happened to be a really good one. She now is a researcher at an Ivy League school. Her postdoc blew her networking wide open.
Be careful to examine where postdocs from both opportunities end up. Network matters a lot in getting your first "real" job. Do not compromise network for one or two extra publications.
*Do note that I would question a postdoc who did his or her BS+MS+PhD+Postdoc all at the same place. It might not be a deal breaker, but it would certainly make me wonder if there are some underlying issues.