Why is the location detection (based on my IP address) wrong?
The location detection shown on whatismybrowser.com is based on a service called GeoIP from a company called MaxMind. They make a best attempt to correlate your computer's IP Address with a physical location (a Suburb, City, or perhaps State, in a Country).
Depending on a number of factors, the results from their database may be very accurate or quite wrong.
Whatever the homepage of whatismybrowser.com says your location appears to be (remember that it also says "Approximate" underneath!), please understand that this is just where their database thinks you are coming from.
The detection shown on whatismybrowser.com is contained to the site and has absolutely no bearing on any other website or system. So if the site is showing that you seem to be coming from a completely different suburb or state, just know that this is what their database thinks.
Why is their database a bit wrong?
It can be quite hard to determine exactly where the traffic is coming from, based on IP Address.
One factor to consider is your ISP - some ISPs route all their traffic to a fairly central location before it reaches the public internet. As such, regardless of where you are actually located, your internet traffic will appear to be coming from the location of the ISP's exit point. This is an infrastructural issue and nothing can be done about it.
When we were with our old ISP, the geographic detection for our office IP was remarkably accurate - only one suburb off (it reported the suburb that contained the ADSL2 exchange). However when we switched our internet to Australia's National BroadBand Network, the geo detection now reports that we are basically coming from the middle of the City, absolutely no where near where we actually are. This is probably because all the NBN traffic is sent to the more centralised location before actually hitting the public internet - thus the traffic appears to be coming from closer to the city.
It's just a best attempt
If you go on to other websites (perhaps a Weather prediction website) and it is giving you the weather for a different location than where you really are, they are probably experiencing the same kind of issue. As discussed already, it's just a best attempt at locating you. The weather website (or whatever) should have some way of letting you selecting your real location.
The detection which we show on the website cannot be changed by us; MaxMind provide a great service and are constantly updating their GeoIP database, so who knows - perhaps in the future they will more accurately report your location.