(Yes, I know, geo IP databases aren't perfect, and people using VPNs will get incorrect results. But for most people, this isn't an issue.)
As an example, something like “pizza near me” should work:
In terms of protecting privacy, you’re right, we don’t need to store the IP address (or any personal data), so we don’t. There’s more detail about how we do anonymous local searches here:
Disclaimer: DuckDuckGo staff.
E.g. if I search for <a href='https://duckduckgo.com/?q=melbourne+restaurant&t=ffab&atb=v1... Restaurant"</a>, the first result is FL.
"Melbourne Indian Restaurant" is a bit better, but half of the front page results are still FL.
"Melbourne weather" always used to return FL, but that looks like its been fixed.
This is what I see when searching from the UK: https://i.imgur.com/XIxo4Jx.png
Quite clearly Melbourne, Australia. Maybe if you're in Florida it'll bias towards there.
(The ad is geolocating correctly, but the first actual search result is "Melbourne Brevard County Florida")