Well, to begin with, you'd enter into New York City. Because that's where Ellis Island is. I suppose there were other ports where immigrants could be processed, and Ellis Island was just the most famous.

But, if we're talking about Ellis Island. There were quite a few options. While a lot of people were coming to New York and stayed in New York (and their descendants are New Yorkers today), it was just as common for new immigrants to fan out across the country. This is personal anecdote, but my great-grandfather arrived from Sweden at Ellis Island, traveled from there to Chicago, and after a few years settled in Mississippi of all places. Ultimately it was the immigrant's choice, though, not assigned.

Some newer or less populated US states would promote themselves to immigrants exiting Ellis Island. They'd tout their rich farmland and plentiful opportunities, often in printed brochures. Some places even gave discounted or even free tickets to immigrants. A lot of immigrants came to the US to farm, so hearing about a place with plenty of cheap land was right up their alley.

A lot of immigrants didn't go too far, though. Pennsylvania and Ohio are centers of Germanic and Slavic culture in the US, for example, and they're only a few days travel from NYC by train.

After a generation or so, a certain place would become known among immigrants for a strong ethnic community. So you'd choose to go there because you knew that you'd be among people who spoke your language, practiced your religion, and had familiar traditions. This is how Minnesota ended up heavily Scandinavian-American, for example.

So there might be things that pulled you in a particular direction (work, farmland, a particular ethnic community, probably also poverty or limited resources), but all in all, the choice was yours.

Edit and TLDR: On the off chance you're in New York, you should absolutely go to the Ellis Island Museum, which is my source for most of the above. They do a great job of conveying exactly what it was like to pass through Ellis Island, and what life was like for immigrants after they entered the US. (For instance there's a whole room full of promotional materials for different states, including brochures with train line maps and timetables, so people would know exactly how to get to North Dakota or wherever from New York Harbor.)