It is an interesting time of year to go to Yellowstone. I went in May, a few years ago. The locals call it the 'muddy season' April might still be pretty cold/ snowy. When I was there only the North entrance was open and a lot of the roads were still closed with snow.
You'll mostly have the place to yourself, just you and whatever animals are out and about.
yeh ive been through there in the summer, its terrible(waaay too many people). ill enjoy it being mostly animals and me. but yeh, most roads are closed. that sucks. cool pics btw