Hi,
There are many cameras that will fill these goals but it depends a fair bit on your ideas of image quality and budget.
The waterproof 'ruggedised' cameras have a folded light path and very small sensors. Their IQ isn't as good as better non-waterproof compacts. OTOH, they may get you a photo in situations and places where you wouldn't get any other camera out of its case. (No-one makes a WP rugged camera with a significantly bigger sensor, though many people wish that someone would just get on with it.....)
In good light, any high-end compact (Canon Gs, Nikon 7700, LX7, XZ2, X20 etc) will do an excellent job and the output will be frameable at 8X10. Several of them have a waterproof housing available if that appeals.
Compacts with small sensors won't do well in poor light, and if you want to cover that you're looking for a camera with a bigger sensor. The Canon G1X has the biggest - a 1.5" sensor - and IMO the best IQ in a fixed zoom P&S style camera. It also has a flash shoe, a VF for harsh lighting situations and a swivel screen. I find mine great for travel, hiking and landscape, but it has to be said that it's a bit slow for sports and action. And it needs an accessory lens to do macro. The G1X would be followed (in IQ) by the Sony RX100 which has a 1" sensor. The RX100 has the benefit of being quite a bit smaller, but you get no VF, no flash shoe and no swivel screen.
I've not gone into compact APSC cameras like the Nikon Coolpix A and the Ricoh GR. They are small and P&S-ish, have a fixed prime lens and very high IQ, but they are relative expensive and don't have the versatlity of a zoom lens. You could also consider the wide range of MILCs/CSCs if you were to move your budget up, but you did say P&S.
Hope this helps. Enjoy your decision-making.
Cheers, Rod