In order to affect an effective invasion of Alaska, the Soviets would have to have certain things happen in advance. A majority of the based forces in Fairbanks and Anchorage would have to be shipped overseas to some place. Without doing that, you've got entirely too much American forces in Alaska. They be able to completely stymie any invasion attempt. You know that addage that they chanted back during the D-Day amphibious invasion? "If the Allies get stopped on the beaches, the invasion fails." Well the same thing would apply to a Soviet invasion of Alaska.
Once certain things happened, and assuming the Soviets were desperate enough and desired to "save a nuke" and use men instead, they could invade. Key places they'd need to take out:
Fairbanks
Anchorage area (yes, the entire area, including the Matanuska valley)
Kodiak Island (at least the major Coast Guard station there)
isolate the Seward Peninsula
Valdez
Tok
Outside of Alaska, they'd need to take:
Whitehorse, Yukon Territories
Prince Rupert, British Columbia
Key choke points, for either side:
Whittier Highway coming out of Whittier and going into Anchorage. Can basically seal off the entire Seward Peninsula this way.
Highway 2 (The Al-Can) that runs from Beaver Creek, Yukon Territory to Tok, Alaska. (Yes, there's an even smaller junction a bit east of Tok called Tetlin Junction that also controls a very rough, dirt road called State Highway 5 that leads up to Chicken, Eagle, and across the border to Dawson, Yukon Territories and eventually Stewart Crossing, Yukon Territories. Take and hold these and you seal the main body of Alaska off by land.
Haines Junction - Whitehorse (both in Yukon Territories). They control the roads that lead out of Southeast Alaska. The rather meager forces in Southeast Alaska would have a beast of a time fighting their way out overland if those roads were taken and held by the Soviets.
Neutralize the airfields at Yakutat and Cordova. They're not military airfields, but they are large and were once WW2 military airfields. No real roads going out of those places to anywhere worthwhile in Alaska, but those airfields could be a very, very good staging point for American forces to get back into Alaska by air. If the Soviets can neutralize these areas, and keep them neutralized, they won't have to worry about them.
Prudhoe Bay. People seem to think if you take the pipeline you control the oil. Well, if Prudhoe Bay stops pumping the oil, the only thing you've got further down is an empty pipeline. Worthless. So if you're going in to get crude oil (not really going to be able to refine much of this at all in Alaska, no major refineries there), you'll need both Prudhoe Bay and key points along the Alaska Pipeline.
Control the Inside Passage. If you take Prince Rupert and can get the Inside Passage mined, you can cut off supplies to the entire Southeast Panhandle of Alaska. They go into starvation and lack of fuel and eventually surrender. Don't have to throw any military into that mess. Any Soviet forces venturing into Southeast Alaska is likely going to be chewed up...by a couple squads of Army Reservists and the wildlife/insect like/plant life.
Now getting all of this done in an expedient time is another task, and probably the most difficult. Gotta start in winter when the ground is hard. Doing it in summer is suicide. Get in, take the areas, set up defenses and hope that the Americas are foolish and attack in summer. (Which they won't, because the Alaska National Guard would tell them what to do with themselves if they were ordered to attack in summer).
So winter offenses only. Hunker down and defend in summer and scrounge, scrounge, forage and scrounge...because you'll need it. It would suck to be the Soviet forces stationed in Fairbanks. Ugh! Cold as you've probably never seen it.
Hopefully this helps a little.
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