The answer is certainly not, "never." Arguably, you could point to two periods in the 20th century when things were relatively peaceful, if not exactly great for everyone involved. The most recent would have to be the period between the two world wars (or, to be more specific, the period from the end of the Turkish War for Independence in 1923 and the invasions of North Africa in WWII). This period was tumultuous because most of the Arab world was under one form or the other of European colonialism -- the Anglo-Egyptian 'condominium' and then British and French mandates in Palestine, Jordan, Syria, Lebanon and Iraq -- but were mostly free of sustained armed conflict, and were an era of rapid state building in most parts of the middle east, to the point where travel would have been as easy, or conceivably easier than it had been to these areas previously. That's not to say things weren't hot, there was a great deal of social upheaval -- a Kurdish rebellion in eastern anatolia in 1925, many protests against the British in Egypt and Palestine, labor strikes, food shortages, all kinds of problems -- but when things did get violent, it was relatively brief, at least compared to WWI and the Cold War era.

The second period in the 20th century would be the era leading up to and just after the 1908 Ottoman Constitutional Revolution. This was a period, before 1908, of relative peace (roughly twenty years), although the government under Abdulhamid II was notoriously autocratic, and vengeful on citizens who crossed him. He also carried out several massacres of Armenians -- casualties in the tens of thousands -- in the 1880s and 90s. After he was overthrown and a constitutional monarchy and parliament were reinstated, the Ottoman Empire -- still encompassing all of the Arab Middle East and big chunks of SE Europe -- enjoyed relative harmony between ethnic and religious groups as the Empire finally seemed on the track towards democracy under the banner of Liberty, Equality and Fraternity. It wasn't to last, however, in part because the economic situation was still really bad (the Ottoman economy was largely controlled by the British, who were attempting to recoup debts from wars that had been fought more than twenty years prior) and in 1911 Italy invaded what is now Libya, a conflict that lasted almost a year, and then in 1912, Bulgaria decided it was time to fight for its independence, and so the Ottoman army pivoted over there. A hop, skip and a jump, it's 1914 and the Ottomans are on the German's side in WWII. But this period, known as the "second constitutional period" is often looked upon with a wistful counterfactual hope -- what could've been if the Ottoman democracy actually worked somehow. And there's a fair case to be made, many figures who would go on to be leaders of violent nationalist movements following WWI -- including the godfather of Israeli Zionism, David Ben Gurion -- were in fact members of the Ottoman Parliament in this period. It's worth pushing back on this kind of nostalgia -- surely things still would've been difficult even if those pesky wars and colonialism weren't around -- but it is often a useful period to emphasize for the reason that it counters the image of the middle east that your question presupposes -- that it's always been a violent, sectarian mess.