I post this question even before I start my PhD in computational biology.
After 3 years of my PhD study, I try to give a proper answer:
Short Answer :
Not only journals but also conferences.
Long Answer
The most thing you should focus on, if you want to design software or algorithms, is the following top conferences:
- ISMB 
- RECOMB 
- WABI 
These conferences publish state-of-the-art ideas of algorithms and software.
Then it comes journals:
- Bioinformatics 
- Genome Research (software) 
- Nature Methods (software) 
- Nature Genetics 
- Nature Review Genetics 
- Journal of Computational Biology 
- BMC Bioinformatics 
- Nucleic Acids Research 
You may wonder: so many journals, how could I handle them.
Again, you need to firstly focus on those top conferences, and there are only three. Try to read all papers on them.
Then, try to follow some new research ideas in Nature series.
Finally, follow articles on these journals for the specific topics you are interested in.
That is my understanding, hope it helps.
                    
                
                 
Hi, start looking here: http://www.biostars.org/post/show/792/which-bioinformatics-journals-do-you-follow/ If you search deeper biostar, you can find a few interesting suggestions.
However, as I just have a computer science background and do know little about biology. I want to focus on specific bioinformatic tools and algorithms specially.