"I just stick with what I was taught in that one year of highschool Deutsch - if the i comes after the e (in a diphthong), it's "i" as in "ice." So "wine-stine."
Yeah, I learned it was pronounced like the second vowel. Thus "stein" is stine, and "stien" is steen.
"Vienna" is "veen," more or less, in German, "das Wien."
Similarly, "wienerschnitzel."