Neocolours

I can't help you much, since I have a DSLR (Nikon D5000) and a cheap coolpix to take to the beach and put inside an underwater casing. So I have no clue about the camera's that fall in between. And Wingsrising allready did a pretty brilliant job explaining lenses.

But I was wondering, since your list of where you want to take pictures is basically both indoor/outdoor and scenery and close up, if a lens-swapping compact wouldn't be an option? Like the nikon 1 J3 (other companies have them too just google lens-swapping compact)
I have no experience with them, and I can't find any American prices (google keeps sending me to Dutch sites and I have to go in a minute) so they might not be an option, but it seemed worth mentioning.

As a side note, I'm quite fond of my polarizing filter for really sunny places with a lot of reflection. (Like beaches) but I don't think they make those for compacts with attaches lenses.

If you want a camera that is more likely to take good pictures in low light, especially if you're anticipating a little motion or handheld-blur, you might not want mine unless you have patience and knowledge to fiddle with the aperture and shutter speed settings (which you can manually set). Mine also has issues with glare from backlighting and sunbursts from light angle. Mine mostly edged the others out on zoom and macro, which are more important to me. Another one of its perks is GPS tagging.

If you're OK with having a larger camera and a few specialized lenses but want to keep costs down, look in the market for a good used interchangeable-lens camera.