Maximum flexibility

If you can score a gently used/refurbished D7000 for little more than D5100, go for it.  Not sure where you live, but most reputable vendors have  D7000 priced nearly twice as much as D5100.   

Yes, D7000 is more advanced and has more pro-like features but D5100 and D7000 share same sensors and the image quality from both are virtually indistinguishable.  D7000 also has internal autofocus motor (not found in D5100)  that allows it to use older, non AF-S designated Nikon AF lenses.  Unless you already have a bunch of these older Nikon lenses, this feature is irrelevant to you.  Is D7000 twice as good as D5100?  Don't thinks so.

Thus far in photography, as technology improves, cameras become outdated more quickly than the lenses.  Therefore, I would use the cost difference between D5100 and D7000 and invest in quality optics rather than cheap kit lenses from get go. 

These are three prime lenses that I recommend to start out with:

1) Nikon 35mm f/1.8 AF-S DX

2) Nikon 50mm f/1.8G AF-S or 50mm f/1.4G AF-S

3) Nikon 85mm f/1.8G AF-S

Nikon 18-200mm f/3.5-5.6G VR AF-S zoom lens is good for everthing else.

Also, invest in a good external flash such as SB-700 and learn fo use the bounce flash technique for improved picture quality, especially indoors.

The D7000 is worth it just for that big beautiful veiwfinder.  Image quality between the two is about the same, but the 7000 gives you way better battery life and TWO memory card slots, which is very handy.  Plus having that screen on top to change camera settings rather than having to fish through the LCD menu is nice.

if you are into photography business - better go for d7000 and that too a new one as the amount will pay off - tight on money and no old lenses - d5100 is competent and both have same image quality

I had the 5100, liked a lot the pictures, but always had to take my eye off the EVF to do any adjustments. This is because it is very menu driven. I repurposed the Fn key to control ISO, which helped somewhat, but still it was far less fast in real world usage than other cameras I use. The D7000 afaik is weather sealed and has better finger controls. Sensor is the same.

I'd always rather buy used or refurbished anyway: the D7000 is worth the upgrade for essentially the same price.

If you were absolutely happy with the D5100 I see no reason to go for something else. The rule of thumb I stick to: don't buy something if you don't know 100% why you need exactly that. Save "a few hundred bucks" and invest it in a better lens or anything else.

If used D7000 is for same price get it, it is worth its functions! 

It is weather sealed

supports auto focus with older lenses

1/8000 minimal shutter speed,

2 card slots

9 cross type focus points

and it fits better to big hands like mine. You will not outgrown your camera so soon and your next upgrade will be hopefully some full frame 

I would recommend the Nikon D7000, I think it offers you more room to grow as a photographer. 

So I ended up with a D7000 - but a new one! Photoprice.ca found me a new body-only D7000 for less than what used ones are costing on eBay. Couldn't be happier.

Used D7000 is better, I think. As far as I know, release time lag of D7000 is 0.052 sec, D5100 is 0.2 sec. I think this will make difference of your photo especially when you take your children's photo. Shorter time lag is better.

D7000 for it has more feature than D5100 and has better ability at low light condition

video mode on 5100 suck , cannot manual . if you use video more than photos shoot buy d7k . :D

Used D7000 I think is better.. ^^