The Long Stone is nice enough and close to the Westin. Turn on to Fleet St, heading east (away from Temple Bar). Keep going until the street changes to Townsend St and it's on your left just before you get to Tara St.

Maybe try The Stag's Head for traditional music, I can't remember if they still do it downstairs there. It's a good pub and worth going to anyway. To get there head west on Dame St (with Trinity College behind you) on the left hand side of the street. There's an alleyway with a mosaic of their logo on the ground, head down that and you're there. If you overshoot the alley (easy to do) just turn left on George's St (at Rick's Burgers (highly recommended )) and then take the first left off George's St and keep going until you see it.

I'd also second avoiding Temple Bar. The only pub worth going to there is The Porterhouse on Parliament St. It's They have another pub nearer to the Westin, Porterhouse Central on Nassau St which is not as good but it does have all of their beers.