That is certainly true; it is very unwelcoming to subject someone to multiple rape (men, young and old, from the city).  While Ezekiel is clear that there were more than simply sexual sins rampant in the cities, the Hebrew word "abomination" which he uses hearkens to that used in Leviticus. Jude provides the early Christian and Jewish understanding of the time that the abominations and perversions of the two cities were anything but being "inhospitable" - were, according to the understanding of the time (and presumably prior), sexual in nature.  Jewish literature enumerates a number of sexual, and other, sins attributed to both cities.  In the full Scriptural context, then, the sin of Sodom seems to be that giving oneself solely to sexual pleasures leads to other selfish acts.  
No. Being merely unwelcoming is the least of Sodom's sins.
My wife's family is 100% Lebanese.  I cannot be accused of misunderstanding the importance of hospitality in Middle Eastern culture.