Static wargame objectives which aren't geographical features seem to me a missed opportunity. How about having them move and interact with the forces and each other?
Here's one possible approach, a simple homebrew example for Warhammer 40,000.
Decide which objectives are living. Each moves at the beginning of the relevant player's turn, at half usual speed in a random direction, but may not assault. If one comes into contact with another, or a unit, it stops, but may move away or through another next turn. Alternatively, a model in contact may move the objective with it without penalty.
After moving, roll 1D6; the objective activates itself on a 6, or on a 5+ if in contact with another objective. If an objective is held by one of the players, the player may opt to activate it automatically now. Roll on the table at first activation to determine nature.
- Specialist - the nearest friendly unit gains a +1 to its cover save or a model with a doubled range and strength and halved penetration on one weapon; decide at first activation; the effect is permanent, but a given unit may receive it once only
- Civilians - replace the objective marker with a unit of 2D6 citizens under the control of the friendly player; the unit as a whole is now the objective, down to the last member, and cannot be activated again
- Controller - the friendly player may choose the individual directions in which his or her objectives move next turn
- Visionary - the objective is assumed to have the parley ability and will attempt to form a new force from all sides, selecting the nearest unit each activation; control of this force is determined randomly at the beginning of each game turn
- Beacon - all of the players gain a +1 bonus to reserve rolls and may reroll any one die in the deep striking process; this objective cannot be activated again
- Annihilation - the objective destroys itself; roll 2D6 for blast radius, with the result on the higher die being the strength and that on the lower the penetration
This way we get the chance of more complex interactions, even among the objectives alone, and a few unexpected events; the landscape comes to life a little more. The only bookkeeping needed is a single die face up by each objective with the activation type.