Dusted off the blu-ray player and popped in Katanagatari. It is pretty.
Togame is so cute and it's a little weird her relationship with Shichika. The sword fight in episode 2 was intense. Not long or drawn out but the guy he was up against was very cool. As far as sword fighting, if you liked the 1st season of Rurouni Kenshin you'll like Katanagatari.
Kiku, this is basically a fighting anime but with style. I can tell this will also be a love story and I'm a sucker for those. I know you're not fond of fighting anime but you liked Basilisk. I think you'll like Katanagatari for the same reasons (beauty, visuals, and story).