The Human Microbiome Project (http://hmpdacc.org/reference_genomes/reference_genomes.php) might be worth checking out. I know some (maybe all) of their data is available through NCBI, but it could be worth a look.
The data access area can specifically be found here: http://hmpdacc.org/resources/data_browser.php
What is nice is that individual microbe genomes can be downloaded, selection can also be made based on a given environment, tissue, etc. You can also download a compiled reference in FASTA format of all sequenced genomes.
Why are you looking for a different database? NCBI is the largest and most smaller databases send in their data to NCBI. If it is a matter of slow (or no) access from your country, you can try EBI and DDBJ, but all three databases are synced daily, so you will find the same samples in all three.
The Broad Institute is a good resource https://www.broadinstitute.org/scientific-community/data. There is also Ensembl http://bacteria.ensembl.org/index.html. And the Sanger Institute http://www.sanger.ac.uk/resources/downloads/bacteria/. I think that these sync with NCBI as well.