Lo correcto es: "Tengo que ir al Starbucks para comprarle un cafe." sin importar si es a él o a ella. Si dijeras tengo que ir a comprarla un cafe, se entendería que es a ella pero no es tan correcto como la primera forma. Ese cambio del pronombre se llama laismo: http://es.wikipedia.org/wiki/La%C3%ADsmo

Lo correcto es, "Tengo que ir a Starbucks ha comprarle un café"

Shawn, I apologize in behalf of Hispanic people. Unfortunately, there are many people here that can't even write or speak their own language well! So, I suggest you DON'T trust all the answers you're given. Your options are just fine, both of them are correct. However, ''a comprarle'' sounds better. When it comes to saying ''al Starbucks'' or ''a Sturbucks'' I'd say it really depends on the region. ''A Starbucks'' sounds better in general Spanish, but for example in Chile, we tend to use articles much more frequently, specially in everyday situations. Being this said, ''al Starbucks'' sounds more natural for me. Hope I helped you.

Tengo que ir a Starbucks a comprar un cafe.

La respuesta de Sebastian está bien, pero "Ha comprarle" NO tiene H