National guard armories would be a sticky issue. Most of everything in them is actually owned by the federal government, but is easily claimed by the state. What I have personally seen is state "authorities" always have contingency plans for seizing National Guard armories and it is not the other way around. National guardsmen NEVER get access codes or clearances to get into say, state police arms rooms, but law enforcement ALWAYS get access to guard armories.

Federal bases remain federal bases, unless there is hostility over the secession. They would be considered sovereign US property, maybe with some limited sharing of jurisdiction, much like the relationship between Gitmo and the rest of Cuba, or more likely, the US bases in Okinawa and the Japanese government. In fact, the states may even opt to quickly engage in an imperial style defense pact with the US so that the troops from particular states are in military units from that particular state and go on deployments with regular federal troops under various treaties, not too unlike the way Canadian troops often deploy with US and UK military forces.

That's the "soft secession" model. We don't need to explain how the hard one goes.