For a historical tour, you don't really have to pay anyone. All of the main sites are right together in Jongno area and you can walk it all in a day and see the Cheongyechon, Insadong, Gyeongbokgung and Deoksugung. For the main museums, just hop on Line 4 to Samgakji (Warm Memorial) and continue south to Ichon for the National Museum.
As far as nightlife, I would recommend Ongno Food Tours. If you're traveling solo or don't speak Korean, going to "real, local" places is sadly almost impossible. I recommend this tour because they go to places in Jongno alleys that are very "local" and even include a stop at the street tents near Jongno 3 Station, a definitely local place. I go there often and always see tourists want to go, but without the guide you wouldn't know what to do or even order.