Selfish logistical issue

Can you guys help talk me through this?

Background: I have two cats, Alex Rodriguez and Blossom (Princess Blossom Pepperdoodle Von Yum Yum), both of whom are around a year old.

My catbox has always been in the bathroom, under the sink. But this is getting to be untenable for a few reasons: 1. The pipe under the sink makes it impossible to have a covered catbox so it's just standing there open, which leads to 2. Blossom kicking litter out when she scratches. So I'm constantly having to sweep up litter from the bathroom floor.

Is there a way for me to stop the litter-kicking problem while still having an uncovered litter box? There's no other space in the bathroom to put the box. Otherwise, where can I put the litterbox that I can cover it? I'm thinking the kitchen hall sort of near the bathroom. Remember that I'm in an NYC apartment that's approximately 750 square feet, with two bedrooms, a living room, a kitchen, and a bathroom.

Also, is there any truth to those self-cleaning cat boxes?

Also, for the two people who sent me cat-related questions two weeks ago: I have no idea. I don't even understand my own cats! (Which is pretty much the point of cats.) I'd take your cats to the vet to get them checked for UTIs, which is what I'd do it one of my kids started peeing or pooping in the wrong places with no other major changes going on.