Red

Ye, blue means that you've done all of the ones youve unlocked but not all in that category. If no NPC has one for you, check your deliveries and also try capturing various monsters to see if it unlocks any arena quests for them. High Rank also has optional quests for hitting HR 100 and for doing all of the other optionals. One of the annoying quests to unlock involves fighting tempered monsters, so go fight a bunch of tempered monsters. I suggest Jyuratodas, Barroth, Pukei... There are guides online that will tell you what quests you still need to do