Good first-time study pre-registration website/service
Looking around, it seems that there are a number of preregistration sites available, but they're not set up in the way you described.


A number of journals seem to have set up their own pre-registration processes, as described in the following two articles: [1] [2]
Some labs publish their own pre-registration papers (see these papers in the Harvard dataverse database).
Some fields are trying to set up pre-registration datasets specific to their field (e.g., political science), and they don't seem to be getting much traction
At least one other site seems to mirror AsPredicted.org in both scope and function: the Open Science Foundation Registered Reports site


All that said, though, it seems that pre-registration is still in its infancy. There are many articles discussing whether preregistration is a good idea at all ([3][4][5][6], as well as [1] and [2] from above), with some pointing out some very significant flaws with the concept. Additionally, while AsPredicted.org seems to be trying to do a good job, not all study paradigms can be encompassed within it's structure.

I fully recognize that your question is asking for a location where you can preregister, and that my answer is getting away from addressing that directly. That's intentional; given that (a) the concept is in its infancy, (b) the concept is nowhere near standard practice for any journal or field, and (c) it's unclear what role preregistration plays in peer-reviewed research anyways, my recommendation would be to simply follow your own lead and write down for yourself ahead of time the types of analysis you intend to perform, and use that as a guideline for yourself. Stated differently, even if you were able to put this sort of information in a centralized database (which doesn't currently exist), you would experience no more benefit than if you just wrote it down in a notebook and stored it in your office.