Main things you can't do are things that involve other hexes. Can't move to other hexes (because of zero move, exceptions possible using Turnamancy). Can't attack across other hexes, including spells and archery.
Planning, communications, some forms of scouting, take-offs and landings of flyers (within the hex or a city you control) are all possible off-turn. You can lay some traps. You can restack all you want.
So you're not completely helpless, which opens up a lot of possibilities (and some problems).
City Zones and Hex Boundaries
Talking about this stuff got us on hex boundaries. Archers and city ballistic engines can shoot across hex boundaries on their turn. But when it's not their turn they can only shoot enemy units in the same hex (or city zone if their side doesn't own the city), or as defense when your city is being attacked.
Same thing goes for some natural attacks like dwagon breath. Can't park your reds on a hex border and fry enemies in the adjoining hex. Breath is blocked at the hex boundary or the boundary of a city zone. Arrows just freeze in midair. I had to go see that for myself.