Do you mean due east along the line of latitude? From the Empire State Building, the first land higher than the top of the building would be the hills of northern Portugal, somewhere in the region of Viseu. (relief map)
Heading west from San Francisco it would be somewhere in Japan, but I haven’t got time to pinpoint it right now.
Heading east from the ESB (443 metres above street level, assuming about 450m above sea level), I reckon the first place you hit on that latitude (40.74843 N) would be about here: Google Maps
That seems to be the intent: “due east…at the same altitude”. No mention of straight lines or one direction. Sounds like flying east at the same altitude relative to sea level and the same latitude.
East wouldn’t mean a great circle, when you fly a great circle your heading changes (except for special great circles such as lines of longitude and the equator.)
He could possibly mean east magnetic, but that would be an odd requirement for a simple question. I think it is safe to assume a true heading.
Fly due east from St. Louis and you’ll run right into the hills in southern Indiana before you’ve gone 200 miles. Fly due west and you’d barely get wheels up before you reach the Ozark foothills.