Stronger Synonyms:
* Ardent: intensely enthusiastic or passionate
* Avid: having or showing a keen interest in something
* Fervent: having or showing great intensity of feeling
* Zealous: having or showing great energy or enthusiasm in pursuit of a cause or objective
Neutral Synonyms:
* Anxious: impatient or worried about something
* Keen: having a strong interest in something
* Excited: feeling or showing a lively interest
* Enthusiastic: having or showing great excitement and interest
More Formal Synonyms:
* Assiduous: showing great care and perseverance
* Diligent: having or showing care and conscientiousness in one's work or duties
Less Formal Synonyms:
* Raring to go: very eager to start doing something
* Hungry: very eager to learn or experience something
* Chopping at the bit: very impatient and eager to do something
The best synonym for "eager" will depend on the specific context of your writing.