Take a look at the map below. You will see 3 arrows locating Seoul station (Landmark of Kangbuk area), Jongno-3-ga Station and Itaewon Station. One of the easiest ways to get to Jongno-3-ga and Itaewon is to use subways (subway system in Seoul is quite convenient). At Jongno-3-ga Station, No1, 3, 5 lines cross so just take any one nearest your hotel. And as for Itaewon Station, No.6 line is the only one going there but No.6 line meets No.3, 4, 5 lines near Itaewon Station so you can easily transfer.
But if you're willing to use a little more money for the sake of convenience, take a cab at your hotel and tell your driver to go to 'Nak-won-Sang-Ga'(for Jongno-3-ga) or 'Hamilton Hotel'(for Itaewon). Quite an adventure? ;-)
For bigger map, click HERE