If denied entry to EU, what US city do they send me to?

Most of the time, if you are refused entry to a country, you will be sent back to the airport from which your flight to that country departed, usually on the same airline which carried you to that country.

For instance, if your itinerary was MEX-JFK-LHR, if you were refused entry at Heathrow, you would be sent back to New York (not Mexico City).

In a few cases I've heard of, immigration officers in various countries have used their discretion to allow someone refused entry to arrange their own transportation out of the country. You should not count on this being available to you, though if the situation arises you can always ask.

Given the EU is a large place with varying policies, I will answer based on the UK and also based on another answer here in Travel Stack Exchange where this has happened.

The question "What are the visa rules for US speakers, at UK conferences, who may be getting paid?" which was triggered by this blog post by Rachel Nabors about her experience being refused entry and removed from the UK, includes an interesting answer from long time Travel SE user and former UK immigration legal adviser Gayot Fow.

In this particular removal, the US visitor denied entry was sent back to the US east coast (NYC) when their origin was Portland. Gayot Fow notes in his response:

The removal

She was served an IS82, which is the form they use when someone does not qualify for leave-to-enter AND their behaviour is inappropriate. It gives them the option, but not the obligation, to have her placed on the Home Secretary's exclusion list (that's a bad thing). They removed her to NYC instead of her base on the USA's west coast. They didn't have to do that, there are flights out to the west coast all the time, but that was just icing on the cake. Minimal compliance.

Emphasis mine.

I cannot find anything in the UK rules which have changed to require removal to a destination which suits the traveller better - removing them to a port of entry they will be accepted at is good enough for UK immigration.

First, it’s unlikely to happen because the airline will try not to let people on board that would be denied entry.

Second, the airline taking you say from London to Berlin where you are rejected, would be fined, and would have to take you back to London. Because that’s the place where you would have been if they hadn’t let you on the flight.

The airline has to fly you back at their expense, but will try to make you pay for it. Your nationality is unlikely to make a difference.

(“At their expense” means immigration won’t pay for the flight, and if your pockets are empty they still have to fly you. Once you are back, they will try to make you pay. And you owe them the money. But if you have no money, you can’t pay them).

This is an old story but it may still be helpful. 1983 so it was not actually the EU but the EEC. Some things have changed but I think that the ones relevant to this question has not.

I had been backpacking around Asia on a very low budget. When my money started to get low, I bought the cheapest ticket to home or close to home that I could. This was on Biman Airways from Dhaka Bangladesh to Amsterdam. My plan was to hitch from Amsterdam to my sister in Copenhagen. On arrival in Amsterdam, I was stopped and questioned at immigration. I was asked how much money I had and I was only able to produce one $20 traveller's cheque and six $1 notes. Even at the time, this was not an impressive amount of money. I tried to argue that since I was Irish, I even had the right to work in the Netherlands. The officer replied that I had not stated that my intent was to work so he did not have to admit me. I claimed that I could get to England where I lived (it was possible) but he said that since I was Irish, he could not be sure that the UK would admit me. If I could not afford to fly to Ireland then he would instruct the airline to return me to Dhaka. Obviously, that was not desirable. My only other choice was to be detained while I arranged for some money to be sent to me. I was put in a cell for three days until I was able to arrange for money to be sent to me. That was not as easy then as it would be today. Once I had enough money to afford a ticket to Dublin, I was permitted to enter the Netherlands. Fortunately, I was not forced to buy a ticket to Ireland. I managed to buy a bus / boat ticket to Ipswich in the UK and it actually cost slightly less than $26. So, I could have got home with my original budget but I would have been very hungry as there was little change from my $26. A final insult was that I was charged for meals and accommodation while I was detained.

In my cell were two other Irishmen. Maybe it was a special Don't let the Irish in day. They were returned to Dublin.

Yes. Thousands of dollars.

First, the airline won't let you board unless your papers are in order (or they pay a harsh fine). But even then, you can botch the entry interview or have a visa problem the airline can't foresee (the airline isn't fined in that case).

At that point, the airline is responsible to the State to remove you from the country (that agreement is not particular as to where). And that can blow up in their face if they remove you to a country that also refuses you. So they try to send you to a place you won't be or can't be refused, e.g. your country of citizenship unless you have right-of-residency somewhere else.

For this removal trip, the airline is responsible to the State to make it happen. However you are responsible to the airline for the cost of it!

And yes, they can send you wherever they please within your country. Least, they're not going to bump a paying passenger simply to get you to an internal destination of choice. In other cases, the destination is impossible: If your itinerary started in South Bend, Indiana, there are no flights from LHR to South Bend for instance.

Many of us who travel rely on bargain fares which are only a small percentage of "full card rate, retail" fares. Naturally since this is last-minute and compulsory travel, you are likely to be stuck paying full card rate for that ticket. They gotcha!

I suspect if you already had a ticket in your pocket that would suffice for the refusal flight, and was timed to be suitable, they would just let you use that, especially if it was with the same (responsible) airline.