If you want the more touristy part of the City, I do recommend staying at the north side of the Han River.
The Metro is fantastic, and there is nowhere you can't go with it

Just make sure you get the city pass and top it up

I stayed in Gangnam and that suited me quite perfectly, but I must admit I did miss the more quiet areas which can be found north of the Han River... But nothing more than a metro trip away.