Have you thought about the ZX-9? Nakamichi corporation itself chose this model (more than thirty of them!) for their own recording studio. I would definitely recommend the ZX-9 over the ZX-7 [I have both.]
The Vintage Knob site has posted the whole brochure for the ZX-9; click the links at the bottom of this page to view it:
http://www.thevintageknob.org/THEVAULT1/ZX9/ZX9.html
You can read some owner's reviews of it here:
http://www.audioreview.com/cat/other/tape-decks/nakamichi/zx-9/PRD_124814_1595crx.aspx
Never owned a Dragon, but I've heard them, and chosen to pass on buying one, at least for now. Given the complexity of repairing them, the premium you pay for their fame (best-marketed of all the Naks, and with a catchy, memorable name) and the fact that the ZX-9 sounds at least as good to my ears, I see no reason to get a Dragon. Maybe one day just to try it and A/B compare it, but the ZX-9 is enough that the "need" for anything else just isn't there.
Some people do say that the CR-7 sounds better, others say the ZX-9 sounds better. I've never heard a CR-7 (yet), let alone compared the two models, so I can't comment. The CR-7 is slightly more automatic (the ZX-9 is purely manual), so it definitely is worth considering. I'd pick a CR-7 over the other two you list, just based on what I've heard about its sound quality, from people who have owned the various models.
The ZX-7 predates the Dragon, which predates the ZX-9. I think Nakamichi pushed the envelope on quality with each release. Not sure about the dates on the CR-7.
The other one you should consider is the 1000zxl. It was Nak's greatest no-holds-barred statement piece, but it is relatively hard to find (the ZX-9 isn't that easy to find, either) and more expensive. It is, allegedly, THE BEST deck Nak every built. I had a chance to buy one a few years back for about $300, and still regret letting it go. It ended up being bought by someone in Singapore and shipped there from Hong Kong!
Overall, I'd rank them as follows:
1000zxl
CR-7 or ZX-9 (close choice)
Dragon (almost as good as the two above; more famous and some might prefer it)
ZX-7 (outstanding on its own, just edged out a bit by the ones above)
If you figure you don't want to wait until a 1000zxl or ZX-9 shows up (which could take a while), then I'd suggest the CR-7 or the Dragon as slightly preferable to the ZX-7. Read up on the two models (audition if possible) before deciding. Ask yourself what is most important to you: ease of use? absolute best sound? number of functions? appearance?
Heck, you can't go wrong with ANY of the models you listed (or the other two I've mentioned) - they are ALL good.

:yes: Any of them will give you "sounds like the original" or "sounds like CD quality" sound. At least for now, I'm still keeping my ZX-7, even though I have the ZX-9, because it IS VERY GOOD, too! You won't feel disappointed, no matter which you get, unless you start making picky comparisons.
All that said, NOTHING beats a top-level reel-to-reel, not even a TOTL Nak deck. The physics works against it, although Nak managed to stretch the presumed engineering limits for the cassette format beyond what was once thought possible, and their top decks DO sound GREAT. You can also get a lot more music on one reel of tape than you can on a cassette. Takes up more room, tape is harder to find, but are you sure you want to go the cassette deck route? Not saying it's wrong; both are great in their own ways, but worth thinking about. Of course, you can always do what many of us do, and get BOTH.