I'm thinking on starting a blades character. Is there a faction a blade could "hide" in that would still be considered lore friendly? So far I was considering the Legion. Would that be a good cover, or not?

Yes. You may want to play a stealthly/savvy character. The dragon-hunting blades haven't been around for centuries.

The Legion is a very interesting faction to join for a member of the Blades - in fact either side of the civil war is an opportunity for characterization. The Companions is a good fit, and while possibly unorthodox, the College is fairly neutral when it comes to the Blades.

It's much harder to explain why a member of the Blades would join the Theives Guild or Dark Brotherhood. The former could be considered a cover, while the latter may represent someone who has adopted an "ends justify the means" attitude, and feels that the near-extinction of the Blades allows for extreme solutions to preserve it.

Any except the DB. While Blades have had assassins in their ranks, the DB and the Blades are at cross-purposes.