Nice Hat/Video Games/Visual Novel

Unlike some other media, in a Visual Novel you can actually see the Nice Hat:

Ama Shigure in SHUFFLE! always wears some kind of cat-eared cap, to the point where Rin wonders if he's ever seen her without one. It hides her ears.
Ace Attorney:
- In the fourth game, Phoenix Wright gets one. It looks just like a ski cap, and it has a hidden camera.
- In later games, Ema Skye gets a cute, Pink Means Feminine hat to go with her glasses.
- Angel Starr has a bento-themed hat. Picture 1, Picture 2.
- Trucy has a top hat to go with her magician style.
- Ini Miney wears a beret that gets abused during the course of the case.
- Olga Orly normally wears a red and white bandanna, but when going undercover as a waitress in a Russian-theme restaurant, she wore a fur hat in the typical Russian style.
Clannad: Ushio (Tomoya's daughter) has two hats, a nice sunhat and a school/sailor hat (the current page image).
Hanako's black flatcap from Katawa Shoujo (second from the left, here).
A number of the women from Umineko no Naku Koro ni have nice hats, such as the previous Beatrice, Eva Beatrice and Lambdadelta.