At that price point, I'd look for a USED Sony RX100 series in as good of condition as you can find (I see several on eBay right around $300). The Sony RX100 was considered high-end P&S a decade ago. If the glass/shutter/sensor is still good then it should still be a good choice.
The Olympus TG series is another option but I'd only go that route if you need waterproof capabilities.
Otherwise, I'd just use a smartphone camera. The low end P&S market is rough. Pretty much all modern smartphone cameras are better than modern low end P&S cameras.