Lately, I've been playing through 2 Minutes to Midnight, a high-level simulation of the Cold War from Plague Island Games and Draco Ideas. I backed this game on Kickstarter when it first came out, and I was very pleased when I finally got a chance to play it. It pushes the definition of a solitaire wargame, but it scratches much of the same itch and I'm thoroughly enjoying it.
Despite fundamentally being a two-sided conflict (US/NATO vs. USSR), the game has a quite strong solo bot that functions well enough to be very challenging against a human player. Like the rest of the game, the bot's actions are card-driven, and the solo deck can be customized to alter the "personality" (focused on expansion, tech, economics) and difficulty of the bot. The game looks similar in concept to Twilight Struggle, but I have found the gameplay to be smooth and fast, able to cover the entire 1950-1990s timeline in about 7 hours, though there are shorter pre-designed scenarios as well.
What I think makes this game shine is the emergent narratives that arise due to the combination of card-driven events and dice rolls. In my current game as the Soviet Union, I was able to gain a strong conventional forces advantage, leading to a successful military operation in Finland/Sweden, flipping them to Communist client states. On the other hand, the Communists were defeated in the Chinese Civil War, placing a neutral authoritarian government on the USSR's doorstep and robbing them of a key ally. One of my current goals is to use friendly governments set up in Venezuela and Guatemala to move toward the Panama Canal, which would shift the naval balance away from NATO.
The game also features a unique implementation of nuclear weapons. In the extensive designer notes through the manual, the designer states the assumption that nuclear weapons can't actually be used because, well, that would make the rest of the game rather dull and not worth playing. However, falling too far behind in the nuclear arms race will lead to your country backing down from conventional conflicts and can create unrest among your populace.
If you're able to find a copy - it doesn't look like there are a ton on the market right now - I'd highly recommend it, whether you plan to play solo or against an opponent