I found a nice AirBnB accross from the National Muesum in the New City about a 15-20 minute walk to the Old Town and a 2 stop ride on the Public Transporation from the Museum stop.
Is this a good area? Its $110 per night for a 2 bedroom Airbnb with a balcony and view of the Muesum and the City. There are shops and restaurants nearby.