Stat-boosting Ranged Weapons

Blue Mage has no throwing skill, but some throwing items provide useful stat bonuses. Items that go in the Ammo slot can be swapped around without losing TP, so you can swap between, say, Tiphia Sting for TP, Olibanum Sachet for physical Blue Magic, and Phantom Tathlum for magical Blue Magic. The Chakram weapons go in the Ranged slot, so equipping one of them resets TP.

1: Happy Egg, Fortune Egg, Orphic Egg
15: Rogetsurin (for pulling)
25: Morion Tathlum (MP+3 INT+1)
30: RSE sachets: Elvaan gives STR+2, Tarutaru gives INT+2, Hume gives +1 of each
40: Junior Musketeer's Chakram +1/+2 (STR+2/3 outside nation's control)
50: Mantra Coin (MP+12)
58: Tiphia Sting (acc+2 att+2)
60: Bibiki Seashell (VIT+4)
61: Death Chakram (from Pulling the Strings solo ENM60)
66: Phantom Tathlum (MP+10 INT+2)
70: Hedgehog Bomb (MP+30 Enmity-1)
70: Lamiabane (Magic Attack Bonus, Refresh)
70: Mamoolbane (Accuracy+6, Evasion+10)
70: Trollbane (Increases Rates of Critical Hits, VIT+10)
75: Aureole (macc+8, drop from Absolute Virtue, Rare)

Damaging Ranged Weapons

Despite its lack of throwing skill, Blue Mage does have access to a wide variety of throwing weapons. Since most jobs do get some form of throwing skill (WHM, NIN, etc), subbing them will give you a decent base skill, with which you can use to pull or deal minor ranged damage from afar without spells.

15: Rogetsurin (AGI+1)
20: Platoon Disc
28: Chakram/[[1]]
40: Junior Musketeer's Chakram (Ranged Accuracy+5, Ranged Attack+5)
43: Junior Musketeer's Chakram +1/Junior Musketeer's Chakram +2 (Ranged Accuracy+5, Ranged Attack+5, STR+2/+3)
57: Moonring Blade/[[2]]
68: Rising Sun/[[3]] (HQ version gives Ranged Accuracy+10)