Seoul and Busan

Hello everybody!

I will be in South Korea from 2 until 18 of September.

What do you think about being in Seoul 5 days and then a weekend in Busan? Do you think that is doable or will be a rush? Would it be a better idea to stay in cities near Seoul?

Also, I have to be in Incheon for one week. Do you have ideas for places to visit?

Thank you! :D