Good stuff! How much time do you have?

Ruined but still wonderful, Clontygora
http://www.themodernantiquarian.com/site/1625/clontygora_court_tomb.html

Ballykeel Dolmen is a classic of the type
http://www.themodernantiquarian.com/site/1749/ballykeel.html

Just over the border is Proleek (your also about 40 mins from Newry to Newgrange, Knowth and Dowth, definitely worth half a day, go early!)
http://www.themodernantiquarian.com/site/1172/proleek.html

And ballymacdermot http://www.themodernantiquarian.com/site/1627/ballymacdermot.html

All three above are within 20 mins drive from Newry.

Further north you have Ballynoe stone circle:
http://www.themodernantiquarian.com/site/1048/ballynoe.html

Legananny Dolmen
http://www.themodernantiquarian.com/site/1055/legananny.html

Giants Ring near Belfast
http://www.themodernantiquarian.com/site/2243/giants_ring.html

which you could take in on a very winding route to Giant's Causeway, or you could go around the other side of Lough Neagh and visit some wonderful sites in Tyrone. There's a handful of excellent sites within a fairly small area:

http://www.themodernantiquarian.com/site/5369/creggandevesky.html
http://www.themodernantiquarian.com/site/2524/dun_ruadh.html
http://www.themodernantiquarian.com/site/2540/beaghmore.html
http://www.themodernantiquarian.com/site/5872/altdrumman.html
http://www.themodernantiquarian.com/site/6731/sess_kilgreen.html

and on the way from there to Giants Causeway you could take in this place: http://www.themodernantiquarian.com/site/2963/tircony.html and possibly here http://www.themodernantiquarian.com/site/3005/craigs_lower.html and http://www.themodernantiquarian.com/site/8383/craigs.html

There's plenty more to see, these are the ones I would take a day tripper to but if you have more than a day or two you could reach a more extensive list.