A Russian visa application requires both an online application and, potentially, the provision of further supporting documentation on request:
- completed, signed visa application
- confirmation of, and register number from, the Uniform Federal Register of Tour Operators of the Federal Tourism Agency (aka "invitation from Russia")
- bank statement (if requested)
- statement from the employer regarding the applicant's wages for the previous 12, 6, or 1 month(s) (if requested)
- certificate of insurance valid in Russia for entire duration of stay (if requested)
- documents regarding the applicant's ownership of property in the country of his citizenship (if requested)
- a certificate on the makeup of the applicant's family (if requested)

This list is the result of the "Agreement between the Russian Federation and the United States of America on simplification of visa formalities for citizens of the two countries"

Obtaining a Russian visa is not a mere formality; it can require a lot of time and lots of planning. While there appears to be no strict requirement to apply in the country of normal residence (the online form allows you to nominate any Russian consulate/embassy for the collection of the visa (and the provision of all further documentation required) it is not exactly a process that is conducive to an "on-the-road" application as the OP seems to have expected. In fact, such an application may even attract additional scrutiny; it is doubtful whether all the required documentation would have been in the OP's possession, or that the visa would have been issued in time for the OP's original plans.