well, it's just physics---usually very small camera = small imager and small lens opening so getting very high image quality out of small camera in ambiant light is a tough battle.
best all round image quality without flash requires a good fast lens.
lots of choices, but for small walk around camera that can deliver pro type guality for web work i would go for oly 5050 or 5060 or canon G series---or a camera that can use microdrive so you can take hundreds of high quality pix.
a little bigger compact camera (fixed lens) like the lumix series is also good.
no substitute for a good lens.
lots of choices, check image samples:
www.dpreview.com