So with the new expansion we have a new secondary profession to work on, Archeology. Now this does not have any immediate benefits to it and it does involve A LOT of travel time. But I come with a few tips for you would be history seekers.
1) Eastern Kingdoms is where you should go if you want to find more then just Fossils and Night Elf parts. The Eastern Kingdoms has a variety of Dwarf, Troll, Fossils and Night Elves. If you go to Kalimdor you will find out Night Elf and Fossils. Now while this would allow you to solve artifacts faster, that is actually a trap.
2) DO NOT SOLVE ANYTHING. At least until you go grey on what you can pickup. For a long time you will be able to skill up on finding the pieces, and since the parts do not go to your inventory you might as well wait to solve them all until you cannot skill up from picking up pieces.
3) If you want to make your life a little easier, get the Add-ons Archy and Tom-Tom. Archy tracks your pieces, and the dig sites for the continent you are on. Tom-Tom works with Archy to give you an arrow to the nearest dig site.
I hope these tips assist your with your trips to dig up the past.