General gaiety:
* Gaiety - This is the most direct noun form of "gaily."
* Cheerfulness
* Joviality
* Merriment
* Lightheartedness
* Vivacity
* Briskness
* Liveliness
* Sprightliness
For specific instances of "gaily":
* If you're talking about a gaily decorated room, you could use decoration or adornment.
* If you're talking about a gaily dressed person, you could use attire or apparel.
The best option depends on the specific situation and the desired nuance.