View finder or not

[bitsnpieces]

That's quite a list you're looking into and I'm sure they're all great.
With regards to viewfinder or not, I really think it's just up to you. What are you used to? I'm personally used to the liveview (I use the viewfinder if I really want to finetune or want to look fancy when taking photos).
You mention the issue about the sun, I know Sony's LCD screens can be very bright so even in sun, you can decently see what you're doing (not sure on the a6000 though, but my a55 and a65 are super bright).

But just one question, you mention that your price range is $900-$1300 - is this just for body (and maybe kit lens) only, and you'll pay extra for lenses in the future, or are you looking for a one-stop solution?

I don't know about the FujiFilm X-E1, but I know the X20 takes amazing photos - my friend had it and I really liked it, so I'm going to say the quality of the X-E1 should be good too.

I don't know what the Panasonic's a like these days, but from scanning through various reviews and comparisons, they're quality is quite good.
I'm sure Nikon and Olympus will be amazing too - which is why it comes back to the question above; are you looking for a one stop solution? Or will you get other lenses?

Purely for lens choice, Nikon.

If it's a one-stop solution you're looking for, may I suggest the Sony RX10? It's a bridge camera with fixed 24-200mm f2.8 lens (so if you're not looking into lens investment, this should cover you for the majority of many things you may do), and image quality is quite good. It's no DSLR quality, but it does a very decent job nonetheless.
http://www.sony.com.au/product/dsc-rx10

I'm sure you can get it cheaper than what's listed above - easily around $200-$400 less.

Anyways, just as a note, only reason I haven't mentioned about the a6000 is because I feel a lot of Sony's recent models are more so to milk their products, rather than providing something of quality. There's problems, and if you're lucky, no problems - if unlucky... Up to you if you want to take the risk or not, but once again, comes back to the question of 1-stop solution, or lens investments.

Also just saw your other post, some very good suggestions in there too.