US schools have public and private dorms- the term hostel does not apply. There can also be on campus and off campus (private) apartments. The dorm room and dining facility will be two separate things- whether or not in the same building (options depend on the school).
There will not be separate dining places for vegetarians. Vegetarian and various ethnic foods availabilty will depend on the specific school. In current times schools usually will have sufficient vegetarian options for a student to have a healthy diet (proteins being the main factor).
When you look at schools that are appealing for the academic fit you can also check out the room and board (dining) options available to students. Often there will be sample breakfast/lunch/dinner/snack bar et al menus. Sometimes Indian foods may be on a menu, alternating with other ethnic foods. Overall menus will reflect the local area/region. Like India (“Patel” sounds Gujarati like my H) there are regional differences such as “grits” in the south.
Do not worry about finding a balanced vegetarian diet. Do not expect many familiar foods. Many/most college/university towns are likely to have Indian restaurants and grocery stores where a student can find comfort foods from home. It is a very different food scene in the US than in India. Part of the experience of attending college abroad.
In the college search be sure to contact the various foreign/Indian campus student groups for answers to questions. These will be found on the website, likely under a student activities heading.
PS- I know the current term “international” is often used, “foreign” is the same and just as good. Semantics, sigh.