Was Freddy Red Beard impressed by the remaining Roman Empire’s infrastructure? Impressed by Constantinople?
I know the HRE didn’t really have a capitol like Rome or Constantinople but did he have any desire to build an impressive city upon his return as the “true Emperor”?
I've answered two similar questions here in the past, so they would be a good place to get started:
and
To summarize, Frederick and Isaac did not get along at all and they never actually met in person. They communicated frequently through letters and ambassadors, but among other things, they both insulted each other by referring to each other with the “wrong” title - Isaac called Frederick emperor or king “of the Germans” and Frederick referred to Isaac as king or emperor “of the Greeks” or “of Constantinople”, while both insisted on being called Roman emperor.
Isaac was also sure that Frederick’s army was there to besiege Constantinople. The crusader and Byzantine armies did have a few skirmishes outside the city, and Frederick may have planned to attack if they couldn't secure passage across the Bosporus (or at least, he may have wanted Isaac to believe that he would attack, even if he wasn't actually going to do it). Frederick always remained in Philippopolis and Adrianople though, while ambassadors negotiated in Constantinople on his behalf. The ambassadors complained that they were mistreated, and the crusaders were also convinced that Isaac was secretly allying with Saladin to destroy them.
Eventually a settlement was reached and the crusader army was ferried across the Bosporus in March 1190. In the previous answers I’ve linked to here, I said that Frederick was only in Constantinople long enough to be ferried across the strait, but I was actually mistaken - the army didn’t cross from Constantinople at all, they crossed further south at Gallipoli. So, Frederick never met Isaac and never even saw Constantinople.
Frederick had accompanied his father Conrad III on the Second Crusade, over 40 years earlier in 1147, but then too, the Germans never entered Constantinople and never met the emperor in person. So whatever Frederick thought of it, we don't know, and chances are good that he felt very poorly about it since his experiences there were always bad. And unfortunately we'll also never know what he planned to do once he returned home, since he died in 1190 while on the crusade.
Sources:
Graham A. Loud, The Crusade of Frederick Barbarossa: The History of the Expedition of the Emperor Frederick and Related Texts (Ashgate, 2010)
John B. Freed, Frederick Barbarossa: The Prince and the Myth (Yale University Press, 2016)