The group running for the Municipality of Beirut (representative of Sunnis, Maronites, Shiites, Druzes). Genes haven’t changed in 3700 years.
Note added in June 2020:The archbishop of Canterbury claimed Jesus was "nonwhite". Under such a definition so would Homer, Caesar, Alexander, Socrates, Aristotle, etc. (East) Mediterraneans were more alike, quite remote from Northern Europeans.
"To pass for a Jew or a Nabatean ["Arabes"], a Roman had to pierce his ears or get circumcized, but to pass for a Gaul he needed to put chalk on his face…" [rephrased] Petronius, Satiricon.
Note added in December 2019: Since I wrote this piece we got overwhelming DNA evidence during 2019 that levantines had indistinguishable DNA from that of Imperial Romans.
Note added in December 2017: We have indication from period literature that Levantines and East Meds looked indistinguishable from Greeks and Romans (as well as emerging genetic evidence) — but markedly different from Northern Europeans. So the idea of qualifying Levantines(Jews and Western Syrians) as "nonwhite" has a yuuuuge cultural effect: it means reclassifying the entire Western Canon before the Renaissance as "nonwhite" (Homer, Plato, Aristotle, Sophocles, the church fathers s.a. Christostomos, etc.) which solves much of the current cultural wars.
The absurdity culminates when one realizes that so many pillars of the Western Canon as Thales, Zeno of Citium, Lucian, Posidonius, Antiochus of Ascalon, Clitomachus, Libanius, Ammianus Marcellinus, Publilius Sirus, (as well as Steve Jobs) etc. were of Levantine stock. (This doesn’t count the Cilicians, Capadocians, Commagenians, Carians, Phrygians, Lycians, etc.).
Note added in July 2017: We now know pretty much how inhabitants of the Levant looked at the time from my colleague Pierre Zalloua’s series of studies (a combination of J2a (some J2b like yours truly), R1a, R1b, E1b1b (Mediterranean) and J1 of the Northern Levant subclade).
A random picture of Lebanese in 2017. We have genetic evidence they are very close to the original population of 3800 years ago. So imagine the church fathers from today’s Levant and Turkey to look like them. If anything the Christ looked like my friend Gad Saad.
The problem with identity politics is that they are fully ignorant of, among other things, history and genetics. And they must be as blind visually as they are intellectually. How did Judeans and Galileans look like at the time of Christ? Not according to your politically driven classifications; and not according to some BS in a 2001 article in Scientific American (based on "scientific" reconstruction of facial features and skin tone from … bones). And don’t assume that Jesus would have voted for neocon hawks, Salafi regime promoters, rent seeking "educated" bureaucrats and state-worshipping IYIs (intellectual yet idiots) — simply, Jesus wanted a separation of the holy and the profane, (see my article here).
No, Jesus was not a "Middle Eastern", that is like inhabitants of the olive-oil free swath of land from Saudi Arabia to Pakistan. Near East (Eastern Mediterranean) is not the nonMediterranean or antiMediterranean Middle East (I wonder which idiot made that classification; the correct heuristic is use of olive oil). Jesus looked like a typical Mediterranean, that is, just like a Southern European, and quite standard at that, as we will see below. The inhabitants of the cities around the Mediterranean, by his time, were already quite similar in looks, even if they didn’t speak the same languages, and (as today, in many cases) much different from those that reside say, a hundred miles inside. And we know how Western speakers of Semitic languages looked like, which is no different from today’s Western Syrians: like Southern Europeans; like generic Roman citizens (although most Jews were technically not citizens at the time of Jesus). Strikingly, Western Syrians (a.k.a. urban Syrians) still look the same today — in my experience they are usually indistinguishable from the Ionian Greeks, Cretans, or Cypriots who are in identity politics called "white".

Josephus (maybe)
First, before we look at the genetic data, let’s consider Jesus’s contemporaries. Josephus (left) would be the closest thing we can find, as we are quite sure that he was a resident of Galilee. Jesus was from Nazareth (close to Tyre, actually many parts of Galilee were owned by Phoenician kings); his parent went Judea so he could be born there; the Roman inscription Iesus Nazarenus Rex Iudaeorum (King of the Judeans) was meant to be ironic since a Nazarean cannot be so. So let us look at how Phoenicians looked like [added: we now have the Phoenician DNA]
Hannibal
Who else than Hannibal, another Western Semite who preceded him by two centuries? I am showing a Southern Italian statue of him; his looks on the statue seem to be corroborated by coins issued when he was alive (but again, both could be wrong). Next look at the Syrians from Homs (Emesa).

Julia Domna (contemporary coin), Syrian from the area of Homs, who married Septimus Severus

Julia Maesa (Homs), her grandson the Roman Emperor Elagabalus (Homs)

Caracalla, half Syrian quarter Punic (left) and his father Septimus Severus (half Punic ancestry)

Two more Syrian Roman Emperors: Severus Alexander, Syrian and Philip the Arab (who was actually Aramean not Arab, from South of Damascus)

Posidonius (left), the great Lucian (right), both North Syrians. Maybe that’s how they really looked like, maybe not; but at least that’s the perception of Syrians at some point in hostory.
A Syrian woman from Palmyra (my own collection, bought at Sothebys in 2001).
In addition to the celebrities, we have hundreds and hundreds of funereal busts from the region revealing how people looked like.
Comment 1. I have a heuristic. If people eat the same, they look the same and use similar body language. Western Turks eat the same as Levantines, Greeks and look the same. The Middle East, say Saudi Arabia has no ratatouille, tyme, oregano, olive oil, hummus, ouzo/raki/pastis/arak, pizza (lahmajun/man2ousheh) etc.
Comment 2. My late father was a medical doctor and a true polymath. He did a PhD in anthropology based on blood types with Jacques Ruffié later at the College de France — it fit his work since he was initially a haematologist. But (something I inherited) he was a closet historian, interested in origins of tribes and population settlements. Ruffié, with Cavalli-Sforza, later started the field of genetic geography.
Blood types/diseases are statistically more robust than genetic studies because of lower noise, smaller dimensionality. I recall as a young child listening to Ruffié and my father discounting the "Semitic" vs "Aryan" thesis: it doesn’t hold compared to the Mediterranean/nonMediterranean one. I remember vividly a conversation with Ruffié saying: "Il y a de l’oligocéphale et du dolichocéphale", referring to head shapes, the latter type he called "Armenian", that is his general term for tribes from the Asia Minor Caucasus region.
Comment 3. The Mediterranean was a unit throughout history: it took less time to sail from Athens to Alexandria than it did to travel in the hinterland. Furthermore, the cities of the Mediterranean are often distinct from the surrounding areas: trading urban areas, for instance, have Armenian, Jewish, and Greek Orthodox quarters, but rarely the countryside (outside of some valleys near a large city).
This idea of the Mediterranean as unit was revived by Sarkozy when he was the French president (he is partly Separdic from Saloniki and has read his Duby); it had been abandoned in favor of "Europe" partly because it had been associated with Mussolini, who (sort of) separated the North (Germanic) from the olive oil, but largely when Islam showed no desire to integrate with the rest. Within Islam, countries like Algeria (who got rid of its Salafists by sending some them to France, and many to the grave) are eager to reembrace their Mediterranean identity.
Looks of Western Syrians — Aleppo reconstruction meeting, January 2017