Vegetarian/Fasting Days occur every month on the:

1st, 8th, 14th, 15th, 18th, 23rd, 24th, 28th, 29th, and 30th lunar day, as well as, every Festival Day.

Festival Days:

First Moon
1st: Yuan Shi Tian Zun's (One of the Three Immortals) Birthday
5th: Cai Shen's (God of Wealth) Birthday Lantern Festival
9th: Yu Huang Da Di's (Jade Emperor) Birthday
15th: Shang Yuan Tian Guan's (One of the Three Guan) Birthday
19th: The Day for Qiu Chu Ji (Student of Wang Chong Yang)

Second Moon
2nd: Tu Di Gong (Land God Festival)
3rd: Wen Chang Di Jun's (God of Culture and Literature) Birthday
6th: Dong Hua Di Jun's (Eastern King) Birthday
13th: Ge Xian Weng's (Immortal Pill Maker) Birthday
15th: Tai Shang Lao Jun's (Laozu - Celestial Worthy of the Tao and It's Virtues) Birthday

Third Moon
18th: Zhong Yue Da Di's (Central Mountain Emperor) Birthday
23rd: Ma Zu's (Goddess of Longevity) Birthday
28th: Dong Yue Da Di's (Eastern Mountain Emperor) Birthday

Fourth Moon
10th: He Xian Gu's (One of the Eight Immortals) Birthday
14th: Lu Dong Bin's (Patriarch Lu) Birthday 15th: Han Zhong Li's (Lu Dong Bin's Teacher) Birthday
17th: Goddess of Midwifery's Birthday
18th: Hua Tou's birthday

Fifth Moon
1st: Nan Ji Chang Sheng Da Di's (South Pole Long Life Emperor)Birthday
5th: Dragon Boat Festival (Duan Wu Jie)
18th: Zhang Tian Shi's Birthday
20th: Ma Dan Yang's Birthday
29th: Ling Bao Tian Zun's Birthday

Sixth Moon
13th: Lu Pon's Birthday
15th: Wang Ling Guan's Birthday
24th: Guan Gong's (Deified General Representing Virtue) Birthday
25th: Lan Cai He's (One of the Eight Immortals) Birthday

Seventh Moon
7th: Festival of the Seven Sisters (Jade Emperor's Daughters)
10th: Tie Guan Li's (One of the Eight Immortals) Birthday
15th: Zhong Yuan Di Guan's (Emperor of Exorcism) Birthday
30th: Di Zhang Wang's (King of the Dead) Birthday

Eighth Moon
3rd: The Day for the Plough God to Descend to Earth
3rd: Zao Jun's (Stove/Kitchen God) Birthday
10th: Bei Yue Da Di's (Northern Mountain Emperor) Birthday
14th: Chang E Festival (Moon Goddess Festival)

Ninth Moon
1st-9th: The Nine Plough Gods Descend to Earth (Seven Stars of the Big Dipper, Fire God, and Earth God)
1st: The Day for the Nan Dou Star God to Descend to Earth
9th: Birthday for Zhang San Feng, Dou Mu Yuan Jun, Chong Yang Di Jun, Feng Du Emperor
19th: Guanyin Remembrance Day
22nd: Tai Yi Zhen Ren's Birthday
23rd: Sa Zu Zhen Ren's (Temple Protector) Birthday

Tenth Moon
3rd: San Mao Zhen Jun's (Three Mao Brothers) Birthday
10th: Zhang Guo Lang's (One of the Eight Immortals) Birthday
15th: Xia Yuan Shui Guan's (One of the Three Guan) Birthday
19th: The Day for Qiu Zu Ascends to Heaven
27th: Bei Ji Zi Wei Da Di's (One of the Four Emperors) Birthday
27th: Festival of the North Pole Star

Eleventh Moon
6th: Xi Yue Da Di's (Western Mountain Emperor) Birthday
11st: Special Day for Tai Yi Jiu Ku Tian Zun (The Blue Emperor)
23rd: The Day for the Nan Dou Star God to Ascend to Heaven

Twelfth Moon
9th: Han Xiang Zi's (One of the Eight Immortals) Birthday
16th: Nan Yue Da Di's (Southern Mountain Emperor) Birthday
22nd: Wang Chong Yang's (One of the Seven Perfected Ones) Birthday
24th: The Day for the Stove God to Ascend to Heaven and Report the Good and/or Bad Actions of People to the Jade Emperor
30th The Day for all Gods to descend to Earth

There are others, but this should suffice.