Mirrorless digital camera recommendation?

I'm looking for a good mirrorless compact digital camera recommendation. I currently have a Sony Alpha DSLR that is a nice camera but just not as great as I had expected. Also, I want something less bulky and easier to carry around. I do enjoy my DSLR for things like hiking or at an event where I'm not going from place to place. It is much to big to carry around on vacation or a night out though. I want a mirrorless for the size and still being able to take amazing, quality pictures. I have looked at quite a few different brands and have liked a few but also found one or two cons to each so I'm having a hard time choosing. I want something that is fast, steady, decent battery life, must have a flash, light weight, changeable lenses, good low light capabilities, preferably able to record, the cheaper the lenses the better. I had been quite interested in the Nikon 1 J1 but I don't like that there are only 3 lenses. I have also been looking at a Sony NEX 5N, but the lenses are quite expensive and I'm leary of Sony since I wasn't highly impressed with my Sony DSLR. My price range is $400-$800. Anyone have any good suggestions or even suggestions of what to stay away from? Thank you!

Added (1). Any suggestions on smaller, more travelable DSLR?

I wouldn't recommend one to my worst enemy.

I wouldn't recommend them either. These EVIL cameras (Electronic Viewfinder Interchangeable Lens) cameras are nothing more than glorified, over rated, way - way over priced pocket toys that don't even have a view finder. For that money you can buy another real camera, a dslr… A much better choice.

Several of the Olympus PEN models are going for super cheap on Amazon right now. They're pretty cool little cameras and stylish too plus you would have money left over for accessories as cheap as they are. If you want something a little more powerful I would recommend the Panasonic Lumix G3 which goes for around $599 for the kit with lens. I like the Lumix G3 because it comes with a built in eye level viewfinder which is very helpful for steady shooting and it has a flip out lcd screen too. Make sure you are looking for the G3 though and not the GF3 which has neither of those features and IMO is not as good of a value as the PEN.

For the J1, there's an adapter so you can use pretty much all of the Nikkor lenses (80+)
however, the adapter is $250, and lenses will cost you another pretty penny (for a good one)

the Sony NEX cameras, in my opinion, are the best mirrorless cameras- highest performance, biggest sensors. With an adapter, you can use your sony alpha lenses on the NEX, so you are not limited to the three lenses specially made for the NEX

Entry level DSLR cameras are as small as they come

now, you might be interested in the new Canon G1x camera, which fits right in your budget, and features a massive sensor (for a point and shoot camera).It's not quite up there with the APS-C sized sensor, but it comes close (1.8x multiplier for the G1x, versus 1.5x (1.6x for canon) APS-C multiplier

If you want a changeable lens camera, you've defeated the purpose of downsizing to a small camera. You'll have a mirrorless camera with 2 lenses, you mind as well carry your DSLR. Get a Canon G12.

I have been looking at the Nikon 1 J1 as well but the package I found comes with two lenses which are the 10-30mm & 30-110mm VR Lens. I'm looking for a package with the third lens referenced here.

You can have a look at Panasonic Lumix DMC-GF2 12 MP Micro Four-Thirds Interchangeable Lens
Pros:
- LCD has great color and viewing angles
- Light
- Stereo video
- Hotshoe
- Responsive touchscreen
- Snappy startup
- Dedicated movie button
- Automatic image rotate
- Flash is mechanically released; you can tilt it up for ceiling flash shots, which is nice
- Surprisingly easy to grip (not great, but better than expected for the slim body)

Cons:
- Menus a bit confusing
- Lens is huge (this is excusable)
- Thumbwheel is a bit stiff
- Flash does not extend high enough to avoid 14-42mm lens; ergo, some shadow appears from the lens
- Flash power is okay
- Camera strap is generic and uncomfortable; plan on getting a better one
- Some special color effects inhibit speed (only the really fancy ones, though)