Thanks, I appreciate your taking the time to reply.
There are no versions of Chrome or Firefox for the Windows Phone. I did try two other browsers, which didn't display that error message but didn't actually figure out my location either.
"Allow access to my location" is turned on for the stock browser (IE). It's not an option for the other browsers.
Please don't spend any time thinking about Windows Phone. I know it's a comparatively rare device and in fact I've only met one other person who has one. I got it under great circumstances (e.g., it didn't cost me anything, I'm not locked into a contract, and my company is paying for the service) but when the time comes to replace it, it won't be with another Windows Phone.