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.
Most likely to least likely
1) Tier 1 Countries either with nuclear weapons or strongly allied (existing treating) with nations with nuclear weapons, List is not limited to this
USA and Nato, which is all of EU, Canada, Australia and New Zealand, Also Japan, South Korea, and Philippines,Russia, China, India, Pakistan, Israel, Iran, North Korea. Also Countries which are very close to a nuclear nation, as it would see it as a very imminent threat, Hong Kong, Bangladesh, Nepal, Bhutan, Mexico, Mongolia Few of the Middle eastern countries, Most of Caribbean, Oceania Islands. Might also include countries which a nuclear power is in war with, Syria, Iraq and Afghanistan. Also countries would defend economical interest like Panama or Suez canal.
2) Tier 2 would be non nuclear countries with immense military power, Brazil, and some South American Countries which are a little stable, South Africa, Thailand, Vietnam, Laos, UAE, Saudi Arabia, Malaysia, Singapore.
3) Tier 3 countries, have very little chance of defeating, with little to no advanced bombers, Countries already at civil war, South Sudan, Eritrea, Ethiopia, Most African countries some north African and Middle east countries, Papa New Guinea, Cambodia remote Islands.
4) Tier 4 Countries which cannot defend, nor would the doom snake be interested as lack resources, Includes North African Countries, Deserts, Antarctica.
If countries would be fighting alone without any allies the list would much more different.