Based on what your Agility and Dungeoneering level is, get level 70 agility (or use an agility potion if you're too lazy), kill Blue dragons at Taverley dungeon. The 70 agility is useful for the pipe shortcut near the dungeon entrance, and the 60 Dungeoneering is useful for the resource dungeon there. There's hardly any people, so it doesn't get crowded a lot compared to outside of the resource dungeon. After a trip, you can either teleport to falador to bank, or exit through the shortcut said before, then run to Falador west bank. There's a broken wall shortcut southwest the bank. I used this method, and I got my dragon claws :D