Hard wiring interior car lights..

I wasn't sure if this was the proper section, but I'll give it a shot.

I bought some interior tube lights. I will be setting them up down under where the foot pedals are. Right now there's a V12 adapter that plugs into the cigarette thing, which is attached to one cord. Is goes to a part with a built in microphone, and a button to adjust the sensitivity of it (the lights flash to the beat of the music), it also has a on/pulsate/off button. Two cords come out of that and go to the two tube lights.

I'm wondering how I can hard wire this to my car, so that there are no visible wires? I would like it to run off of my car battery, and shut off when my car does. As well as possibly being directly connected to the radio so that the microphone doesn't pick up on the car noises, or voices.

Also... Where does this go? Can it go in any light spot in my car? As in, there is a light on the ceiling, and also one beside each door, can this go in either spot?

Not good with cars at all, sorry.