Typing a response, and I asked, "What are you looking forward to do in Chicago?". Is that correct, or should I instead ask,

"What are you looking forward to doing in Chicago?"
Use 'doing'.


The "to", here, is a preposition (not the infinitive particle to) hence the gerund "doing" after it. Infinitives

don't follow prepositions; nouns, pronouns, and verbal nouns (-ing forms) and noun clauses do.