I'll make it easy for you: You want a (used) Sony RX100 III.

https://www.amazon.com/Sony-Premium-Compact-F1-8-2-8-DSCRX100M3/dp/B00K7O2DJU

The RX100 was the beginning of Sony's takeover of the entire camera market, from enthusiast level all the way up to full-frame pro cameras. They somehow now have a bigger market share than Nikon OR Canon. I don't know what possessed them to decide they wanted to be The Best Camera Company, but right now they're it, and the RX100 is one of the reasons.

In your shoes I'd go for the RX100 III, they switched from a 28mm-equivalent to a 24mm-equivalent on the wide end which is a non-trivial difference for taking landscape shots. It's $650 new but you can find a ton of used ones for $400ish.

Obviously the RX100 IV, V, and VI have upgraded features but I don't think any of them would be worth it for you on that tight of a budget.