Now, this is an interesting question. The Real (plural: Reales) is a unit of Spanish currency used from the mid-14th century to 1864, when it was replaced by the escudo, and then by the peseta in 1860 (Wikipedia). The word, however, still had meaning: a real was one-fourth of a peseta, similar in function to the U.S. Quarter-Dollar coin. Since "Hills Like White Elephants" was published in 1927, this latter definition would have been the meaning in the story.
The girl looked at the bead curtain.
"They've painted something on it," she said. "What does it say?"
"Anis del Toro. It's a drink."
"Could we try it?"
The man called "Listen" through the curtain. The woman came out from the bar.
"We want two Anis del Toro."
(Hemingway, "Hills Like White Elephants")
Four reales at the time would be one peseta, so the next issue is to find out how much the peseta was worth compared to the 1927 U.S. dollar. Exchange rate data is hard to find; the official U.S. Gov website only seems to go back to 1990, while a different website seems to have all currencies except the Spanish peseta. Today, the peseta has been replaced by the Euro, so all exchange rate databases want to convert the old-time currency into the new modern currency.
After a long search, I believe I have found a reliable source: norges-bank.no, a bank website from Norway. They have a data page with various exchange rates, and they have data from 1914 onwards. For 1927, the USD-ESP exchange rate is:
USD$3.92 -- ESP Pts62.82
If I'm reading this correctly, that would be 62.82 pesetas to each 3.92 U.S. dollars. The exchange rate remains roughly stable throughout the year of 1927, only fluctuating a little each way.
So, to get the final exchange rate, we must find a base. First we divide pesetas into dollars: roughly 16 pesetas per USD$1.
Each peseta is worth four reals, so 64 reals also equals USD$1. One sixteenth of one-dollar's-worth of pesetas is four reals: one sixteenth of one dollar is 0.0625 cents.
Therefore (whew) the total cost of their two beers in 1927 was about six cents. And just for fun, adjusted for inflation, those same two beers, at the same exchange rate, would cost about USD$0.81 today.