For age:
* joven: young
* nuevo: new (can also refer to something being fresh or recent)
For other meanings:
* nuevo: new (can also refer to something being fresh or recent)
* moderno: modern
* actual: current
* reciente: recent
Example:
* Viejo coche: Old car
* Coche nuevo: New car
* Casa vieja: Old house
* Casa moderna: Modern house
The best opposite will depend on the specific situation and the intended meaning.