Medieval Dublin or the 'Old City' is compromised of some of Dublin's oldest monuments such as Christchurch, Dublin Castle and St. Patrick's Cathedral. With the construction of these structures dating as far back as the 11th Century this is truly the old heart of the city.
Nowadays however, while still drawing in a strong tourist crowd, the Old City is representative of a new wave of creativity. The art school NCAD sits near Christchurch and some trendy, student oriented bars such as U Bar have popped up. Meanwhile the Vicar Street venue plays host to a broad range of gigs and performances throughout the year.
If it's a taste of medieval Dublin that you're after however then spend sometime in Christchurch Cathedral or Dublinia – a recreated Viking style Dublin replete with characters to help you get into the swing of things – which are sure to give you a sense of the authentic roots of the area.