What is a Buddhist ceremony or service called, and what day of the week is it likely to be?

If it is a Thai temple (eg. 76-16 46 Ave Elmhurst), the service is where the devotees chant to (take refuge in) the Buddha, Dhamma & Sangha, request the five precepts, generally offer the monks food, and receive a blessing in return, including sprinkling of water, as described here: https://www.yelp.com.au/biz/wat-buddha-thai-thavorn-varanam-elmhurst & here: https://www.facebook.com/pages/Wat-Buddha-Thai-Thavorn-Vanaram/137256256319623

A Vietnamese temple (2222 Andrews West Bronx) would probably have the same service, such as shown in this video: https://www.youtube.com/watch?v=Hwo4JBbpraw

It is best to go to an Asian temple (rather than a meditation centre or even a Zen centre, since meditation & Zen centres are usually run by Westerners & may not do food offerings & blessings) because a traditional Asian service involves an 'exchange' of devotion between the monks and the people. That said, a Zen centre may do a ceremony followed by meditation. You needs to check with your teacher whether 'personal meditation' is a 'service'.

Taking refuge, food offering & blessing service would probably occur on the weekend but could occur each day. Contact the temple & have fun.

Assuming Manhattan College is in Manhattan, here is a website for an SGI-USA center which is in the Lotus Sutra/Nichiren tradition, The New York Culture Center. It is in the old Cooper Union building at 7 E. 15th Street, New York, NY 10003 (bet. 5th Avenue & Union Square West).

The website's calendar shows a variety of meetings throughout the month, not only on weekends. There are various names like World Peace, Chanting, Lecture, and Intro to Buddhism. Other meetings are by interest group. There are also meetings in people's homes called Discussion Meetings. The World Peace Prayer meeting would probably be a good experience for a beginner. There's chanting with quite a few people which is pretty cool followed by a program which varies. People would be open to speaking with you before and/or afterwards. The intro meeting would of course be good also and is usually focused on Q&A.

SGI-USA is a lay organization so no priests with robes. People dress in whatever way is normal for them. Since your class is on discrimination note that one of SGI-USA's core principles is non-discrimination. This principle is based on the historic Buddhist opposition to the caste system in India, and more specifically on the Lotus Sutra's teaching that all people may attain Buddhism. Even women. This results in SGI-USA having a very diverse membership unlike many Buddhist denominations. As such, attendees reflect the diversity of the area, including the LGBTQ community.

In early times, (and still today in some Buddhist countries), laypeople would intensity their practice on certain days according to the lunar calendar. The special weekly Buddhist holy day is called Uposatha and it is observed on the new moon, the full moon, and the quarter moons. https://en.wikipedia.org/wiki/Uposatha

Today, particularly in the West where we don't use a lunar calendar, you are more likely to find a weekly, bi monthly, or monthly meeting at a fixed time. At the Laotian temple I attend, everyone is invited twice a month to a Sunday morning service which runs from about 9:00 am through about 1:00 pm. The most significant parts of the service include taking refuge, reciting the precepts, and offering lunch to the monks. In our tradition (Theravada), the monks don't eat anything after noon. So the lunch offered is quite a big event and an opportunity for people to give dana.

But Buddhist meetings and services are not uniform and can be scheduled for purely practical reasons. A temple in my area has a Sunday morning service in Vietnamese and a Wednesday evening service in English. Another has a Sunday morning service in Korean and a Saturday Day of Mindfulness in English. Some groups meet for meditation and others meet for something that is more similar to worship.

Best suggestion would be to call or stop by the monastery to see if they have services or events open to the public. The one universal rule is that shoes should be removed before you enter a monastery or temple. Have fun and be well. :)