The first thing I would do is check to make sure that my clothes are invisible with me. If they're not, then I stay inside because ew. If they are invisible, then my first plan of action would be to go and play Pokemon GO, as people wouldn't see me and wouldn't judge me (my town hates the game). I'd also go to school and say "here" at attendance, as it would be interesting to see the reactions. I'd probably go and eat at a restaurant before going and freaking people out with a few basic-ghost tricks.
I'll probably go outside and actually be myself for once because I wouldn't have to worry about people looking at me and judging me. I would be able to get a good look around my city and be able to enjoy myself without constantly wondering whether I am making a fool of myself or what other people are thinking about me.
Depends on how hot it is outside. If it's our regular hellweather, stay inside as usual If it's decent out, go to uni and literally haunt the science building, pretending I'm a ghost. There's enough random shit in the science building that that would keep me entertained for a decent length of time.
"Professooooooooor, my beakers are levitatiiiiiiiiiing, is that supposed to happen???"
Honestly, I'd probably just use it to pull pranks on people...
I mean, there's a lot you could do, like sneak into people's homes, get free stuff, but in the end, I don't do those now for reasons other than "they might see me" so in the end being invisable would be kind of boring after a while.
White. I would go with blue if black/grey/white are off limits, though.
While I personally find really white rooms to be minimalistic and boring I also feel like it's the only thing that wouldn't annoy me after a while. I love the colour blue a lot, it's calming and looks very nice in rooms, but overall I think a more neutral colour is good, and black tends to make rooms feel smaller, while grey just kinda looks tragic to me, so yeah.
Well if everything would be only one color, I'll try to choose a relaxing color. Even if I prefer dark blue, I would probably go with a light blue, that would look like the sea. It would be sad though because I really like the contrast of colour and I'll miss it a lot.