Crystal tower maybe. The ilvl 80 equips from there are good enough for most content, and you get a nice amount of myth tomes to buy ilvl 90 gear while you're at it. You could just keep all the tomes until u have maybe 3 pieces of CT gear, then buy the remaining body parts with the Myth tomes. Don't be tempted to buy jewellery with the myth tomes before you have the left side of your equip window all at least ilvl 80-90.

I think its a better idea to gear the BLM, as being an ilvl 55 tank partied with i90+ party members could be tricky? I don't know anything about tanking but that's my assumption. It's very little problem to do a dungeon with a fresh 50 dps, but its a lot harder with a fresh 50 tank accompanying party members with high dps. . However, you could also go CT on your tank and not take tanking roles with high responsibility. Another option would be to roll on tank equips in CT while on the BLM.