What is the equivalent in English for 情怀？
It depicts a glimpse of private sentiment, or the emotional affinity that draws a person towards certain people or things. 情懷（情怀） is a very subjective term in the sense that it points to something essential within a person, that marks his or her individuality. The feeling can be subtle but it is always expressive; never the kind of private sentiment that is shy, covert or concealed. 
The《漢語大詞典》gives three meanings for the term, ranging from very personal feelings to manifest disposition (English translations are my own): 


  
  心情：personal feelings 　　唐杜甫《北征》詩：「老夫情懷惡，嘔泄臥數日。」 　　Tu Fu is not in a good mood because he's been bedridden from vomiting and diarrhoea for
  several days.  　　郁達夫《過去》：“兩旁店家的燈火，照耀得很明亮，反照出了些離人的孤獨的情懷。” 　　The bright
  lights from the shop-houses is contrasted with the loneliness of those
  who are leaving.  
  情趣、興致：interest, enthusiasm, proclivity, a delight in things 　　清袁枚《隨園詩話補遺》卷五：“劉郎去後情懷減，不肯紅粧直到今。” 　　The maiden in question has lost
  interest declined to wear make-up ever since the male lead, a youth
  named Liu, left her. 
  猶胸懷：disposition akin to high-mindedness 　　峻青《海嘯》第二章：“為革命事業而獻身，就是你畢生的高尚情懷。”    Self-sacrifice for the noble
  cause of the Revolution is a testament to your high-mindedness.