We should clarify whether you mean "plans to" as to "they wanted to do it" versus "they had contingency plans on what to do if war broke out." They definitely had the latter, as the USA definitely had plans to invade the USSR in such a situation as well. Did they have the former? That's a harder thing to grasp, but most of the post-Cold War evidence shows a USSR more interested in maintaining existing borders, maintaining a buffer of friendly nations (Warsaw Pact), maybe making some of the other countries nearby more favorable to its policies (e.g. expanding the buffer a bit or making the edges less "hard"), but not as aggressively expansionist as the American Cold Warriors feared. Whether this was because of deterrence or because they tired of war or some other reason is harder to separate out. We also now know that some of the apparently expansionist policies of the postwar USSR, e.g. in Korea, were less about Soviet ideological desires and more about local pressures (Stalin had to be badgered into supporting the Korean War). (On this sort of thing, Gaddis' The Cold War: A New History covers a lot of ground.)

As for whether they thought the USA would invade, they were definitely of the opinion (hard-earned in Russian history) that having well-armed enemies on your borders was a dangerous thing. They were surrounded by hostile powers, and by the 1950s the USA had ringed the with nuclear-armed bomber bases. The USA definitely had plans (in the contingency sense) for how to utterly eradicate the USSR, and had been making these since 1945. The leadership of the USA and USSR both believed that their enemies were essentially interested in exploiting any weakness and would seek to destroy them if they got an opportunity, so both went to extreme measures to make sure there was no such easy opportunity. We know that planners in the USA did occasionally float the idea of preemptive strike (why wait, if it was inevitable?), and I wouldn't be surprised if their counterparts in the USSR proposed similar things (though the USSR was not at nuclear "parity" with the USA until the 1970s).

None of this involves planners in either the USA or USSR rubbing their hands together and saying, "oooh, I can't wait until we have boots in Washington/Moscow/Paris/etc." It was of a more subtle order of things. The Soviet position was not very different from the American one, in as much as they both desired geopolitical security, they both were willing to manipulate other nations (including subverting democracy) to achieve this, that they both felt intensely threatened by the other and were willing to go to great lengths to oppose the machinations of the other.

The USSR absolutely had plans to invade Western Europe, and one location featured pretty prominently -- the famous Fulda Gap (in Germany). This bit of geography would have been a prime route between Eastern and Western Germany as it would have been a conduit for tanks or other armed forces. Two paths made up of lowland areas (like the Kinzig Valley) were obvious places forces would go through (and in prior conflicts, it was in fact used in this manner, such as during the Napoleonic War or during WWII). The Soviet 8th Guards Army was one of the main forces that sat across from the NATO forces aligned against them. Both sides trained and prepared for a number of scenarios centered around this area.

Here's a 1987 Los Angeles Times article that talks about the Fulda Gap: http://articles.latimes.com/1987-03-01/news/mn-6926_1_fulda-gap

Edit: Here are some previous threads that I found after a quick search, they all seem relevant and interesting:

https://www.reddit.com/r/AskHistorians/comments/y5cg8/what_were_natos_defensive_plans_for_a/?

Huge mega-thread on Russia/USSR: https://www.reddit.com/r/AskHistorians/comments/1b42v1/wednesday_ama_russia_and_the_soviet_union/?