So I was wondering, should there be any problem between Orthodoxy and this part of my secular life?
Oh my goodness, no. In no way, IMHO! We should be ready to appreciate the beauty and goodness in all cultures. There are so many wonderful and beautiful accomplishments that have come to pass in the history of Western civilisation. "....Whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable--if anything is excellent or praiseworthy--think about such things." ( Philippians 4:8 ) We just have to be careful not to swallow all of the precepts on which various civilisations are based, and to do our utmost to baptize the wonderful elements found in all human culture. It is an extremely difficult tightrope to walk between the temptations of sectarianism and modernism (just accepting whole-hog our culture's values without separating ourselves from these values) but I believe this is what we are called to do: it is part of our witness (martyria) to the world concerning the Truth.
For more about this kind of tension that we face as Orthodox Christians "in the world but not of the world", I would recommend looking at some of the essays in Fr. Alexander Schmemann's book Church, World, Mission: Reflections on Orthodoxy in the West
By the way, I share your admiration for Renaissance architecture. I remember how glorious and wonderful I found it just to stroll through the city of Rome several afternoons, in glorious full sunlight and to admire the elegant simplicity of the buildings and fountains and squares. I think the West has a lot to teach us about things like public spaces and architecture. Of course, I find so much to admire in architecture in Orthodox countries as well!