I only recently returned to reading fantasy, except for George RR Martin, who I continued to keep up with during my break. I haven't yet gotten around to reading Mieville or Lynch, but in the last 2-3 months I have read Abercrombie's 5 novels, as well as some others that you may or may not have read such as Weeks' 4 books, Sanderson's Mistborn and Way of Kings and the first three novels of Glenn Cook's Black Company. I definitely enjoyed Abercrombie's works, and while I sometimes had trouble putting his books down, his stories still paled by comparison imo. The others were interesting to varying degrees as well. But none came close to ASoIaF (A Song of Ice and Fire) for me.
Perhaps I just haven't yet found the right books, but so far Martin is unquestionably on a much higher level. His characters are believable and complex and where he takes many of them will surprise, if not shock, you. His world's history, and many of the details contained therein such as heraldry, religion and genealogy, are quite well developed. The political intrigue is fascinating and multi-layered. The scope of the story is Epic, and I don't use the word lightly.
Your concern should not be that you will find anything about this story traditional or mundane, but that after reading this, you may well find everything else to be so.
As has been said, the usual route for new readers is to jump right in with the main books in order:
A Game of Thrones
A Clash of Kings
A Storm of Swords
A Feast for Crows
However, there have also been a series of short stories published, called The Tales of Dunk and Egg. Those are set in the same world, but well before the above four books. To date there are three, and those are:
The Hedge Knight published here:
http://en.wikipedia.org/wiki/Legends_(book)
The Sworn Sword published here:
http://en.wikipedia.org/wiki/Legends_II_(book)
The Mystery Knight published here:
http://en.wikipedia.org/wiki/Warriors_(anthology)
I read The Hedge Knight first, and it gave me a bit of a feel for Martin and what I thought to be a nice introduction into his world of Westeros. It is not nearly as weighty, eventful or Epic as A Game of Thrones, but if you really are wary of reading Martin, then starting with that story (and perhaps one or both of the subsequent Dunk & Egg Tales), might be a good way to ease into this world.