where?
Emphatic interrogative, stronger than どこ. Often used in rhetorical questions or when demanding an answer.
こんな時間にどこだって行くの？
Where on earth are you going at this hour?
どこだってそんな話を聞いたの？
Where did you hear a story like that?
Emphatic 'anywhere', similar to どこでも but with a stronger, more colloquial tone. Often used in affirmative statements.
See also: どこでも
お金さえあれば、どこだって行けるよ。
As long as you have money, you can go anywhere.
He's the kind of person who can sleep anywhere.
Combination of interrogative どこ (where) and the emphatic particle だって (even, also). The だって here derives from the copula だ + とて, an old quotative/conditional particle, giving a sense of 'even if it is where' → 'anywhere' or 'where on earth'.