I tend to skill up *ALOT* of weapons and here's what I found to be rather useful.
0-80ish Clippers in Qufim give great skill during these levels and you can drain/aspir in the unlikely event that you need HP/MP.
An alternative to Qufim would be the area right outside of Rabao, assuming you have the levels to compete with the things out there. The worms, spiders and anticans right there can easily take you from 0-100+. When you get low just dip back inside Rabao and chat with your Nomad Moogle to refill your HP/MP then continue.
100~130 Nest Beetles in Crawler's Nest are great for this range. I stopped at 130 with Axe, Great Axe, Sword there to go to the next area I'm going to talk about, but I would imagine you could get into the 140s on the beetles. This can be easily soloed by a DRK 60+ without any downtime.
110-150? Desert Beetles in Western Altepa Desert (near Revelation Rock) I'm right at this point with 2 of my weapons and skillups havent ceased yet, so Ill have to edit this when I go skill up again. You can do this solo, but its alot easier with a partner.
Around this time you can also start helping with Genkai I and get great skill into the 160s as well.
160-200 Kuftal Tunnel fighting Robber crabs and Sand Lizards. The skill up here is great until 185 or so then it really starts to slow down, I stuck through it (seeing how I was trying for the Arondight) but I would reccomend going to Cape Terrigan or Boyanda Tree and fighting the Crabs there, they are slightly higher level.
From here, I usually stay in the Boyanda Tree and fight Steelshells for skill.
This is great for 200+. I dont want to put a cap on when it gets bad, but I do know the 75 PLD who was trying to skill up Great Sword was getting decent skill into the 240s. It is really easy to get a party for this, as alot of people will want Parties to unlock Weapon Skills.
An alternative here that a WAR friend showed me was fighting Manticores, Wyverns and Toramas in Onzozo. I wasnt getting much skill there at 200, but the rest of the group around 215 skill said it was great. You also have the benefit of fighting several NM's while you skill up if you so choose (in case you want that ugly Assault Jerkin).