In my opinion, it wouldn't prioritize the most military-capable nations, but rather smaller nations which wouldn't incur the wrath of a nuclear power, and expand into many Doom Snakes, also it will realize nuclear war is imminent and use large scale smoke in mask its location. If it is fighting a nuclear power it will use cities and other populated areas, to avoid a nuclear attack.
Almost all of the nuclear nations in our planet are capable of ICBM, once within range, (Russia, USA, and China have worldwide range) will take it about 30-45 minutes to hit the target. MIRVs for multiple targets/ creating decoys and SLBM for quick repose if nuclear submarine is near by. List of countries with nuclear capabilities under NATO include Belgium, Germany, Italy, Netherlands and Turkey (Needs permission/approval). Other than that Israel, India, Pakistan, North Korea, USA, Russia and China all have nuclear missiles.
No country would use atomic weapons as mines, even the crude ones (Pakistan, North Korea) use it with a bomber, there are also few artillery nuclear weapons if combat is much more closer. Even Non-Nuclear countries would be able to defend it with heavy artillery and bombardments, wouldn't not be as effect as a single nuke, but modern warring nations would decimate it with shear raw force because planes/Jet are much faster and better at warfare than a terrestrial object.
If a nanite-AI capable of what you describe exists, it would easily defeat human forces, even with nuclear weapon with a different more tactical strategy.