Servers such as google will keep your location saved for quicker loading times.
I suspect you are confusing two different things. Geo-based load balancing uses a combination of DNS tricks and routing configurations made in conjunction with your ISP (or their upstream provider) for specific major networks (google, akamai, AWS, etc). Your router won't have an effect on how traffic is routed once it leaves your LAN. At most you could set it up with some weird DNS servers that may change how DNS load balancing occurs.
BSSID databases on the other hand, are often way out of date. Google apps for instance will use a BSSID database to attempt to get a more accurate location. Apple does the same.
For the problem OP had - as others have said, resetting your wifi settings, toggling locations, etc may fix the problem. If that doesn't work, it may just be an outdated BSSID database. In that case no need to get a new router, just wait for it to fix itself.
In the past I've heard that you can flag your location as inaccurate in Apple Maps and that will update their database, but I'm not sure how accurate that is these days.