Hello, Roniya. I visited Ireland in January '08. I don't know what your health is like, but within Dublin I was able to cross the metro area of the city, going from the train terminal to St. Stephen's green, in about twenty minutes on foot. There are numerous buses, but I only used them to leave the city.
As for touring, I recommend visiting Glendalough. (Glen-duh-lock) It is an ecclesiastical site dating to around the 600's, shortly after the first Christian missionaries came to Ireland from England. There were once families of believers living there for safety during Viking raids and persecution, as well as a hermit who lived in a cave (still extant) and taught those who came to see him. The location is gorgeous, serene, and features trails that lead to six ancient church sites, and even a Roman arch from earlier yet.
Glendalough is just a few hours from Dublin. The ride is beautiful. There is a bus that leaves St. Stephens Green twice a day I believe, and will bring you back in the afternoon or evening. Bus tickets were, I believe, $15. I don't think visiting Glendalough costs anything, but there is an An Oige hostel (An Oy-Guh) if you plan to stay the night. It's about $20 a night and 5 star. In fact, An Oige's are in several cities.
http://www.anoige.ie/
Here are some photos from my trip, if you're curious:
Glendalough:
http://focusfirst.blogspot.com/2008/03/glendalough-ireland-day-2.html
http://focusfirst.blogspot.com/2008/03/glendalough-ireland-day-1.html
http://focusfirst.blogspot.com/2008/03/glendalough-panorama.html
Dublin:
http://focusfirst.blogspot.com/2005/01/ireland-trip-08-dublin.html
http://focusfirst.blogspot.com/2008/03/return-to-streets-of-dublin.html
http://focusfirst.blogspot.com/2008/03/aer-lingus-wingtips.html
Ardee & Dundalk:
http://focusfirst.blogspot.com/2008/02/ireland-trip-08-days-1-4.html