There are three kinds of sources that are very useful to study a country's views of another: foreign affairs documents, the press and diaries.

You might want to read letters of ambassadors to the Russian court. I don't know what language you know but the Earl of Malmesbury's , James Harris, correspondence to the Secretary of State for the Northern Department Lord Suffolk is available online. See his letters from 1778. Harris was sent to Russia to evaluate the possible benefits of a Russian alliance against France in the American War and as such he reported on "materialistic" issues more than anything else. You will not find much about the Russian culture for example. Another source that could interest you are the correspondences between Diderot, Voltaire and Catherine the Great.

You should consider searching various newspapers and gazettes depending on which years you are interested in. For newspapers you might have to rely on a library or university access.

Finally, diaries of travelers to Russia, for example those of young aristocrats performing their Grand Tour, can be useful. I think of the memoirs of Lady Elizabeth Craven who was presented to the Great Catherine.