Ireland itinerary help

I'm flying to Dublin in mid-August, and have 13 days, excluding the overnight flight at the beginning and the last day when I leave. My flight lands very early in the morning (6-7 am), so I figured I'd hop a bus to Belfast for the first couple days (I see buses leave straight from the airport). I would spend about 2-3 days at the end in Dublin.

In between, I'd like to explore more of the countr(y/ies).
I would love to find a couple places I could spend a day hiking (long hikes are fine, but no overnight). Places that have multiple options of shorter and longer trails and interesting/unique features are preferred.
I'm also interested in history, museums, castles/estates/interesting buildings/etc., sports (any on?), wine/beer. I don't like clubs, and I don't use hostels.
No car, but willing to walk a few kilometers if necessary.

Any recommendations for places I should visit?

IMO, looking at your interests, the Wild Atlantic Way and in particular the north-west might be of interest to you. It is less touristy in the north-west and more rugged but I have done any walks up there. Search the Irish Times newspaper for 'walks' and it will pop a regular feature they have in their weekend paper - I've done a couple and their good. Other walks? There a couple of good ones at Glendalough which can be a day trip from Dublin and Howth, again near Dublin. An iconic Irish walk is Croagh Patrick which is a religious pilgrimage for some but more a test of endurance involving scrambling over loose shale towards the peak (and coming down is worse).

IN Dublin, in terms of museums and buildings, I recommend Chester Beatty Library, Marsh's Library, St Michan's Church (check website for vault tour times as this is the main reason for visiting), and The Four Courts (you can' take pix but it is a nice piece of architecture and history).

In terms of sports you are deep into GAA season of hurling and gaelic football. I think you'd be best off looking to see a local game. I follow a football team called Corofin who play in Tuam and its great to watch. There is no drinking at these games.

Places for drinks? The country is crawling with them. In Dublin I recommend O'Donoghues in Merrion Row near St Stephen's Green, The Cobblestone in Smithfield, Dawson's in Dawson St, McNiells in Capel St, and Keogh's off Grafton St. For local ales try The Black Sheep in Capel St.

This is a paste from a previous post:

I am of the opinion that Dublin needs a good solid two days. One centring around the west end and sights like the modern art museum, St Michan's Church (check online for tour times as a tour of the vault is a key part of the visit), the Guinness Storehouse, Kilmanhaim jail, Phoenix Park/zoo (the zoo is the 2nd oldest in western Europe and has a very strong breeding programme with lots of newborns) and Collin's Barracks (more likely a selection of).

The second day centrally to include the national gallery, Merrion Square, the Kildare St archaeology museum, Chester Beatty Library, Trinity College/Book of Kells, Temple Bar, Grafton St and St Stephen's Green. IMO, the Guinness factory and the Book of Kells are not worth it (particularly price wise) but visitors seem to come away satisfied from visits to both.

St Patrick's, Marsh''s Library and Christ's Church Cathedrals are between these two 'sections' of the city and can be done in either.

This post has been removed because it may not have met our community guidelines.

Thanks for the tips.
I'll look through them and see if I can cobble together a reasonable itinerary.

In terms of sports you are deep into GAA season of hurling and gaelic football.

I would really like to see hurling. Where would be a good place for this? (e.g. places that have multiple teams and play often, good teams, etc.)

If you don't have your own transport, you could join a hiking group for a walk in the Wicklow Mountains. There's a few groups online. They tend to band together cars so you'd get a seat in someone's vehicle. Glendalough has numerous hikes. The problem is getting there without your own transport. Howth has some nice hikes (get the Dart or a bus to Howth) or Greystones to Bray walk (Dart or bus it).

Croke Park in Dublin would be the best place to see a hurling match. It should be easy enough to get tickets providing it's not an All-Ireland or big big match.

This - http://www.gaa.ie/fixtures-and-results/national-fixtures/gaa-hurling-all-ireland-senior-championship/month/2014/08/ - will tell you about what is on, all TBC at this early stage, but not where. TBH, while I love Croke Park, it holds 80,000 and would be battling on most occasions to get half that number in meaning the atmosphere can be a bit hollow (although if it is a Dubs game you could maybe get onto the HIll). Also you feel further from the game and that is not what you want. A game at Semple stadium in Tipp (which hold 53k) or Dr Hyde Park (which is 18k and has a better atmosphere - well, it does for GAA football games and I can't imagine hurling is different) would be better options if possible. In terms of the 'best teams' that is going to be the senior championships and there is only one team per county.

How's this for an itinerary?
Night 1 - Belfast
Night 2 - Belfast
Night 3 - Belfast
Night 4 - Derry
Night 5 - Derry
Night 6 - Galway
Night 7 - Galway
Night 8 - Cork
Night 9 - Cork
Night 10 - Waterford
Night 11 - Dublin
Night 12 - Dublin
Night 13 - Dublin

I figure I can make day trips from each for natural areas, castles, etc., and visit the Giant's Causeway between Belfast and Dery and the Cliffs of Moher between Galway and Cork (is that reasonable? Are there places to store luggage at each?).
Suggestions/alternatives appreciated.

Both the GC and CoM have had new visitor centre's added in the past few/five years and I haven't been to either since then but the old centre's didn't have so you may need to check on their websites. I might suggest 3 nights in Belfast is a lot. What you could do is a night in Bushmills and take in the GC and the rope bridge on a day tour the day you arrive (if you get there early enough in the day) and I'm sure your accom would hold your bags until check in.

IN terms of hurling, the final is Sept 7 and I don't think there will be tickets available or other games on this weekend.

Thanks for that.
I figured one of the nights in Belfast would be to allow a day trip to Carrickfergus, or do you think this would be easily covered in two days with Belfast?

Ftr:
The Giant's Causeway visitor center has a few lockers. Just ask the people at the front and they'll take you over (they lock and unlock).
The Cliffs of Mother gift shop has a small storage cage in the back where bags can be left. Again, just ask and they'll take you back.