I have a new favorite journal: Communications in Applied Mathematics and Computational Science. I just published a paper with them for the first time (technically it's still in press, but you can download it here (paywall) or here (free; same version).
CAMCoS is a hidden gem -- it is relatively new (6 years old) and not yet as widely known as most established journals. I believe that within a few years it will be as coveted a publishing venue as any applied mathematics journal. Here's why.
A respected publisher with an exceptional editorial board. We all know that a primary consideration when submitting an article is the prestige of the publisher and the journal. CAMCoS is published by Mathematical Sciences Publishers (MSP), a non-profit run by mathematicians for mathematicians; they also publish Annals of Mathematics, Geometry and Topology, and a number of other excellent journals. Their website says "our aim is to transform scientific publishing into an industry that helps rather than hinders scholarly activity", and their actions back that up. The CAMCoS editorial board is an outstanding group of some of the world's leading applied mathematicians; take a look for yourself.
Timely and thorough peer review and copy-editing. A respected publisher and a famed editorial board are nice, but how well is the journal actually operated?
My experience with CAMCoS puts it far ahead of most other journals I've dealt with. We submitted the article in early July, and it came back in early November: 4 months, which is not lightning-fast but not too shabby. The referees seemed to be well chosen and to have done a thorough job, suggesting several valuable improvements. We resubmitted in late November (minor revisions) and the article was accepted five days later. We submitted the TeX files in early December, and received the galley proofs with copy editing one month later. The really astonishing part: we approved the proofs on January 7, with one added correction; our article was made available online, in final form the next day, on January 8. I've never before experienced or even heard of that kind of turnaround from a publisher. For comparison, my SISC paper that was accepted in August still hasn't been assigned an issue or a DOI (it's now mid-January).
Electronic PDF features that no other publisher I know offers.
The copy editing is high quality, but what really blew me away is that the copy editor went through our bibliography and made every paper title into a hyperlink to the published journal article. As if that wasn't enough, he added links to Mathematical Reviews and Zentralblatt for every article that possessed such entries. These hyperlinks are active in the PDF, as are hyperlinks from references in the paper to the bibliography, references to equations and theorems, etc.
This may seem like a small thing, but I think it's very powerful. It means that as you read through the paper, when you see a citation in a sentence that puzzles or interests you, can just click on the citation, which will take you to the bibliography. Then you can click on the bibliographic entry to go immediately to the paper cited, or a to a review of it! Click through to the paper and try it for yourself. This is a capability that all journal articles obviously should have had for the last 15 years, but this is the first publisher I've seen who understands that.
You can choose whether to keep your copyright, and you can post the final version of the paper on your website or institutional server. MSP's publishing agreement has two options: if you wish, you may sign over your copyright to them. You will still retain the rights to "reproduce [the article] by any means for educational and scientiﬁc purposes ... without fee or permission" as long as you don't try to charge anyone for it. Alternatively, you can retain the copyright to your work, granting MSP only a license to publish; the only restriction is again that you can't charge others a fee for accessing your work. Their policy has clearly been designed with the author's interests as primary concern.
(Virtually) Diamond open access. Diamond open access is the OA movement's dream; a model that avoids the author charges of Gold OA while still providing peer review and a stable DOI (which green OA often lacks). In strict terms, CAMCoS is not diamond OA, since it requires a subscription. However, I claim it is virtually diamond OA, for two reasons. First, CAMCoS uses a moving paywall, under which articles become OA after one year (thus, only the 2012 issue requires a subscription at present). During that first year, open access can easily be provided by the author posting a copy somewhere.
By way of disclosure, I have no affiliation with CAMCoS and no reason to promote them except that they represent the kind of journal I think the applied mathematics community should support.