All two things are right, but it's up to the context. This is the problem of the ambiguity of the sentence.

I would say your sentence has the meaning of #1. Consider these similarly structured sentences with different meanings. 1. 내일은 친구 만나고 서점에 갈 거예요. => Tomorrow, I'll see a friend, and go to a bookstore afterwords. 2. 내일은 친구 만나서 서점에 갈 거예요. => Tomorrow, I'll see a friend, and go to a bookstore with him/her. 3. 내일은 친구 만나 가지고 서점에 갈 거예요. => similar to #2, but more colloquial and emphasizes the connectedness. -고 connects two actions which are considered distinct from each other. -서 implies the two are part of integral activity, so meeting someone to do something is typically expressed with -서. 가지고 makes this integrality even stronger because it denotes "with/using the result" of the first action.

내일은 친구 만나고, 서점에 갈 거예요 is a little ambiguous sentence. It is better to use some adverb like 혼자, 같이 1. Tomorrow I'm going to meet a friend and after I'm going to go to a bookstore. 내일 친구를 만나고 나서 혼자 서점에 갈 거예요. 2. Tomorrow I'm going to meet a friend and we're going to go to a bookstore. 내일 친구를 만나서 같이 서점에 갈 거예요.