General Enthusiasm:
* Ardently: With intense feeling or passion.
* Avidly: With great eagerness and enthusiasm.
* Fervently: With great intensity of feeling.
* Keenly: With great interest or desire.
* Warmly: With a friendly and enthusiastic manner.
Impatience:
* Impatiently: Unable to wait; restless.
* Anxiously: With a feeling of worry or nervousness.
* Longingly: With a deep desire for something.
* Desperately: With a feeling of great need or urgency.
Anticipation:
* Expectantly: With a feeling of anticipation.
* With bated breath: Holding one's breath in suspense.
* In anticipation: Looking forward to something with excitement.
Specific Actions:
* Ravenously: Eating with great hunger.
* Greedily: Desiring something very much.
* Thirstily: With a great need for something.
* Relishingly: Enjoying something very much.
Figurative Language:
* With open arms: Welcoming something wholeheartedly.
* With a leap: Doing something with enthusiasm.
* Head over heels: Extremely enthusiastic about something.
The best synonym to use will depend on the specific context and the nuance you want to convey.