I just went in for the D5300 this weekend, after some thought and I'm impatiently waiting for it to arrive. I was considering the D7000 but with a decent lens, it would still be more expensive. The D7000 is a pretty old camera now, and the D7100 is too, to some extent. The performance difference between the D5300 and D7000/D7100 really isn't very obvious. I mean you see more differences between the D3000/D3100 and the D3300. The D3300 for example, is really impressive for its price, especially when you're clicking ISO1600/3200 shots.
There have been many improvements on the processor and image quality that make the D3300/D5300 worth it. Besides, the D5300 has WiFi which is limited, but there are 3rd party software that let you control aspects, and possibly transfer data directly to your PC. I'm not banking on that, but if it works, great. There's also 1080p60 video recording which both, the D7000 and D7100 don't have. The D7100 costs a lot more, and you can go in for the D5300, and use the money you saved on more glass.
Only real reasons to spend that much more for the D7100 are two memory card slots, two jog dials, dedicated lit screen at the top. The D5300 is some 44k with a kit lens, the D7100 is over 70k as far as I know, for just the body.