I think the problem with taking this sort of viewpoint is that it's not really how the Russian government would have thought at the time.

From the perspective of 1859-1860 - the Russian Empire had just been defeated in the Crimean War by a coalition led by the British and French, who at the time were the world's hegemonic superpower and wannabe superpower, respectively. That war did not see action in Russian America, but it did have a Pacific Theater that saw action, notably in the siege of Petropavlovsk-Kamchatsky on the Kamchatka Peninsula. The defeat demonstrated to Tsar Alexander that there was an urgent need for modernization and governmental reform, which led to, among other things, the emancipation of serfs in 1861, affecting some 23 million out of 74 million people in the empire.

Russian America itself was extremely peripheral to all of this. The Russian population in Alaska was only a few hundred, and after abortive efforts at Fort Ross in California there was no Russian-controlled area on the North American West Coast that could adequately provision large settlements in Alaska. The original purpose of the Russian American Company, much like with Siberia, had been the fur trade, in Alaska's case especially in sea otter furs. By the mid-19th century fur stocks had been severely depleted, and the Russian American Company was in a bad financial situation.

Now we can look at the situation in the rest of North America. In the 1860s the United States was going through its devastating civil war (it's worth pointing out that the emancipation of some tens of millions of serfs in the Russian Empire went about much more peacefully than the emancipation of some four million slaves in the US) and Reconstruction. The Russian Empire was largely supportive of the Union, with Russian naval vessels visiting San Francisco and New York (some have boosted these as decisive interventions in the Civil War - I wouldn't go that far, but they definitely were public displays of Russo-American goodwill). Russian officers even volunteered to fight for the Union, most notably (and infamously) Ivan Turchaninov, or John B. Turchin, who ultimately became a Union Brigadier General.

Anyway, that was only part of the North American turbulence. The Trent affair in 1861, part of the US Civil War, led to increased tensions between the US and Britain, and the stationing of several thousand additional British troops in Canada. 1861-1867 also saw the intervention of France in Mexico and the installment of the Hapsburg Maximilian as a puppet monarch, backed up by French forces.

Which is all to say: the Russian government, looking at the geopolitical situation, would see two hostile powers with additional forces in North America, and a threatened-but-victorious friendly power in between in the form of the United States. Russia itself was seriously preoccupied with internal reforms, and was in (notional) possession of a sparsely-populated North American area that was basically a financial drain to maintain - and on the border with Russia's main adversary, Britain. Getting cash in return for transferring ownership of this area to a friendly country (that also was on bad terms with Britain) seems like a pretty good deal for Russia, and there's a reason that for so long there was common opinion that the US had gotten the worse end of the bargain.

A final note is that I need to stress how far Alaska is, especially from a mid-19th century perspective, in Russian terms. the Diomede Islands may be a few miles away from each other, but effective distances between major centers are much greater - it's about 2,000 miles from Anchorage to Petropavlovsk-Kamchatsky, and Sitka (which was the main base of Russian operations) is 2,500 miles away. And that base in Kamchatka in turn is some 1,500 miles from Vladivostok (founded in 1860 from territory recently annexed from Qing China), and all of that in turn was months of slow travel away from European Russia. Siberia itself was often very loosely and notionally controlled by Russia (the Chukchi weren't really conquered until the 20th century) and far from the centers of power - steamboats and railroads on a very local scale in parts of Siberia were very new projects, and the Trans-Siberian Railway itself was not even envisaged as a project until later in the century (and not opened until 1904). Siberia itself was not really developed until well into the Soviet period, especially with the first Five Year Plan, and from that time it has provided plenty of gold, fossil fuels and fish for the USSR/Russia on its own.

In short - from the perspective of the 1860s, it was a good deal for Russia to sell Alaska to the United States. Even from a longer term perspective, it probably would have been a strategic drain on Russia, could very well have been lost to Russian geopolitical rivals, and even if it had remained in Soviet control by the mid-20th century would at best have provided resources that the USSR was developing in Siberia anyway.

ETA - on top of all this, it's not like Russian America had clear, defined borders. There had been a dispute between where the border was with British possessions (basically the Hudson's Bay Company) since the 1820s, and this wasn't fully resolved by the US and Canada until 1903. The Russian American Company and HBC had basically a working relationship on the ground, but again from a bigger geopolitical perspective it's not like Britain wasn't in the habit of using boundary disputes to expand its colonial possessions - which would have made defense of the territory by Russia even more of a liability if matters came to a head.