Moofpi has the right outlook on pivots.
As far as movement options go, mastering perfect pivots will help a lot. Mario has really good tilts so pp tilts are a great tool to have in your kit(made easier by having cstick set to tilts).
I recommend using tap jump in conjunction with tilts on cstick. This way you can perform double sticking which makes Mario feel much more agile and precise to control imo. The control scheme can take some getting used to and might not be for everyone. The control scheme prevents accidental jump cancelled upsmashes while allowing for frame perfect short hopped aerials. The precision I spoke of comes from the facts that retreating aerials are made super easy and that with less inputs(which is what happens with double sticking) and the mobility gained from tilts on cstick(aerials done with smash stick cancel your momentum if used during the wrong times of a jump, that problem is gone with tilt stick). You can basically jump in any direction while performing any aerial you want.
Wave bouncing was mentioned. Breversing in general is important.
I use his cape sometimes to stall above my opponent that has been conditioned for an approach. If cape is used backwards, you can stall and follow up with a back air. If not done backwards, nair.
Don't forget about wall jumps. Also, if you run and pivot into the edge of the stage, you get an extended slide where any action can be performed.
Sorry if some of this stuff seems off topic. I know the thread is about movement options, but I figured I could also share little ways Mario's default movement could be made easier too.