Going to Ireland Sat - Monday but my friend had to bail early (going to London before) and I already booked everything. What to do for a 21 yr old solo female traveler? Staying at a hostel so should meet some people but want to have my own plan either way! Thanks!
A good way to get orientated to the city when you first get there is to take a free guided walking tour. They aren't "free" essentially, since it's good practice to give your guide a tip at the end (5-10 euro is sufficient), but they're relatively inexpensive and very informative! Most hostels can easily get one organized for you.
Here's a 2 day itinerary from the Ireland guidebook that might give you some more ideas:
9:00 Visit the Book of Kells and Old Trinity Library ahead of mid-morning crowds.
11:00 Take the guided Historical Walking Tour.
12:30 Browse Grafton Street, have lunch there, or picnic on St. Stephen’s Green.
14:00 Head to the National Museum: Archaeology branch (closed Mon).
16:00 Visit the Jeanie Johnston Tall Ship and Famine Museum.
17:30 Return to hostel, rest, have dinner.
19:30 Go for an evening guided pub tour (musical or literary).
22:00 If you still have the energy, find a pub with live Irish music.
9:00 Tour Kilmainham Gaol (reserve ahead; opens at 9:30 Sept-May).
11:00 Take the Dublin Castle tour.
13:00 Grab lunch.
14:30 Follow the self-guided “O’Connell Street Stroll” in this chapter, taking in the GPO Witness History exhibit en route (in the General Post Office).
Evening Options: Catch a concert, a play, the storytelling dinner at The Brazen Head (or one of the other recommended dinner shows), another guided pub tour (musical or literary), or more live folk music in a pub.
If some of the things mentioned above don't appeal to you, you can always replace it with a tour of the Guinness Storehouse if you like Guinness. It's pretty touristy but the view from the bar from the top gives a nice view of the city and you can pour your own beer (1 included with your ticket). Otherwise, if you want something more outdoorsy you can rent a bike and take a spin through Phoenix Park, which is a huge park west of the central city.
I'll second the list given by Stephen except that, depending on how quickly you like to go through museums and other self-paced sights, you may not get to everything on the list. The RS guidebook uses the star system to set priorities (3 stars, don't miss it -- 1 star, optional) which is very helpful.
There's a walking tour of the Trinity College campus with an optional Book of Kells add-on. This is separate from the Dublin city walking tour -- which is stated as 1.5 hours but ours ran more like 2.5 to 3 hours and went all over town. They both originate at Trinity College. I've done both and found them very enjoyable, weather permitting. The tour guides are in your age group and very entertaining as well as informative.
The National Museum has three locations in Dublin and all are excellent. Also the museums are a good place to get out of the rain if need be.