I was looking at a globe today and it looks like Russia shares a close border with North America. I wasn't aware of this. Why didn't they discover such a large land mass so close to them for that long and even migrate to/explore it? What happened? Am I missing something?
It is expected that human settlement of the Americas happened over the now Bering strait, something like 30,000 years ago.
This is however not relevant to your question. It is important to remember that up until Portuguese and Spanish discovery and settlement of the Americas, Russia as we know it today as a modern nation, didn't exist. The Tsardom of Russia wasn't founded until 1547, and even then, the Russians didn't explore, conquer and settle Siberia (and thus the close straits next to America) before the 17th century. On top of that, major Russian exploration and mapping of the Alaskan coast didn't happen until the Danish naval officer in Russian service, Vitus Bering, led two expeditions to map out the Alaskan coast in the middle of the 18th century.
But do of course remember, that the Russians did settle in North America, and sold Alaska to the United States in 1867.
Because Russians were not anywhere near the North America in 1492.
Arguably, they did; to my knowledge it is generally accepted that most Native American peoples descend from nomads who migrated from Siberia to Alaska over a land bridge, now underwater, during the last Ice Age. Another flippant answer would be that Russia didn't exist in 1492, only the "Grand Duchy of Moscow" (aka Muscovy.)
But the simple answer to what you're actually asking is that Siberia, the eastern part of present-day Russia, was not yet under Russia's control during the Age of Exploration. See this map depicting Russia in the 15th century. The "Paleo-Siberian peoples" to the east refers to tribes such as the Yakut, who are semi-nomadic hunters and fishermen. As might be expected, most of these peoples are not prolific sea voyagers, and I don't believe there is any evidence of contact between them and Alaskans during the pre-Russian period.
That said, don't discount the achievements of the Russians in New World exploration too quickly. Vitus Bering carried out some remarkably productive expeditions to Alaska while in Russia's employ; his comrade, naturalist Georg Steller, described a vast amount of Alaskan flora and fauna including several species that were extinct by the time other naturalists got there.
