Sanna, Yemen lies 495 miles southeast of Mecca.
Asuncion is the capital and largest city of Paraguay. It is located 660 miles miles southeast of Sucre, Bolivia.
There is no such city. The numbers do not work out.
Mexicali, the capital city of the Mexican state of Baja California, is located 300 kilometers southeast from Los Angeles. No capital city is located 300 miles southeast of Los Angeles. Phoenix, Arizona is 360 miles east of Los Angeles.
Riyadh is 270 miles southeast of Bahrain.
Phoenix, Arizona is about 287 miles southeast of Las Vegas, Nevada.
Brussels, the capital of Belgium, is 200 miles east southeast from London, England.
Belarus
Traveling to Mecca from Kansas City, Missouri in the USA, can be accomplished by flying either West or East.
Capital City Airport is located near Harrisburg. More precisely, Capital City Airport is located 3 miles southeast of Harrisburg, Pennsylvania which is the capital of Pennsylvania.
"The capital city southeast of Los Angeles" is not a well-defined term, so it's impossible to answer the question as asked. Mexico City is "southeast of Los Angles", if we're not too picky about the definition of "southeast". So are most of the capital cities of Central and South America. (So is Miami FL, for that matter.)
The first Islam State Capital was Medina, then Damascus, then Baghdad. Never Mecca was an Islamic state capital although Mecca is the most sacred Islamic city.