You should avoid the mirrorless cameras others have suggested. They're a format of compromises, smaller size but you don't have a proper viewfinder (which makes a huge difference setting up a shot), you don't have proper controls to adjust settings easily while you're shooting, etc.
I disagree, with the caveat that
any camera involves compromises; you just have to decide which features are most important to you, and which compromises you can live with.
I was in a similar situation to the OP. I've been using digital point-and-shoots and, most recently, my iPhone's camera, since 2001. However, in the 1980s and 1990s, I had a Minolta Maxxum 35 mm SLR, several lenses, and a flash, which I'd lug aroung in a backpack. I loved my rig, but I got tired of the bulk and weight, so I switched to digital point-and-shoots when they became affordable. Earlier this year, I became interested in more serious photography again, and I decided to buy a mid-range interchangeable-lens camera. I was leaning toward a DSLR-size Sony SLT-A65, because I could use my old Minolta Maxxum lenses with it, but then I remembered why I stopped using my Maxxum in the first place. I didn't want to start lugging around a heavy backpack again.
After reading many, many reviews, I decided that a mirrorless APS-C or Micro Four Thirds camera was right for me. I ended up getting a Sony NEX 6, which offered the best bang for the buck in terms of still-image quality, video quality, and features. It's well built. It's small: with the kit lens, it fits in a jacket pocket. It uses the same APS-C sensor as the Nikon D7000. It doesn't have an optical viewfinder but it does have an excellent electronic viewfinder, which many people (not all) prefer to an optical viewfinder. The advantages are that you can see depth of field, effects, and exposure setting in real time, and other useful information is displayed. An optical viewfinder won't let you do that.
By all accounts, the Nikon D7000 is an outstanding camera. The image quality slightly beats the NEX 6's at some settings. Battery life is better. You have more controls on the camera, because the camera is bigger. The NEX 6 is better at video, though, if that's important to you. Still image quality is great. The electronic viewfinder might be better (again, it's a matter of opinion.) And don't underestimate the advantage of a smaller, lighter camera.
I'm not alone in my belief that mirrorless cameras are the future. The Olympus OMD EM-1 (a Micro Four Thirds camera) is getting raves as perhaps the best non-full-frame camera currently available. It would have cost me an extra grand, though, which I couldn't afford. And the about-to-be-released Sony A7 and A7R full-frame mirrorless cameras are also getting raves from early reviewers. They're smaller, lighter, and less expensive than full-frame DSLR competitors. Time will tell how they behave in real-life use, but more are sure to follow from Sony and from other brands.
In short, check out some different cameras, and see which you like best. You'll find very opinionated people on forums who will tell you that one brand or format rules, and the rest are crap. Pretty much any decent digital camera
these days will allow you to take great shots. Pick something that you like, start taking pictures, and learn about photography. If you outgrow it at some point, you can always upgrade. Good luck to you!