Breakdown of Вчера я посетил Большой театр.
Questions & Answers about Вчера я посетил Большой театр.
посетил is the perfective past of посетить, which describes a single, completed action (“I visited the Bolshoi Theatre once, and finished that visit”).
посещал is the imperfective past of посещать, implying repeated or continuous visits over time (“I used to visit…, I was visiting…”). Since you mean “I went and completed that visit yesterday,” you choose the perfective посетил.