Neither is the subject (it is being used as a pronoun). It is generally singular, as evidenced in the sample usage at dictionary.com. So you should go with
No, neither of these websites is biased, as they both give a wide range of good information without being one-sided.
Note, however, as recorded in another EL&U questionanother EL&U question, that the pluralization depends on which two entities are being compared. In this case you are comparing one website with another website, so the singular is clearly called for; but if you were comparing one group of things with another group, the plural could be used:
Neither the Smiths nor the Wessons are available for dinner.