Welcome. We can always use another bicyclist here.
hmmm..... I haven't experienced all of the states, of course. But I've looked over a number of them and I can make decent guesses about the others. Even then, I'd have a hard time recommending any particular place. I'd say that you could just about choose a region at random and have a pretty good time.
But maybe you could work with the conditions that you can or cannot tolerate. For instance, if you would have a hard time living with hot and humid conditions, then you would not want to visit practically anywhere east of the Rocky Mountains in summer. The south-west would be warm as well, but less muggy.
If you crave mountainous conditions, then perhaps Montana or western N. Dakota would be good. It might still be warm in the day, but it would cool down morning and evening. But I'd stay away from about October to May.
If I were to choose a season and place, then maybe I'd go with Ohio east of a line, roughly, from Cleveland to Columbus and south, sometime around late September through early November (but no later than that). You would find there, mostly, trim and pretty countryside, mostly pretty good roads and nice weather. The further east you go, the more mountainous it will become. If you crave long climbs, then that's nice. But the roads will get worse.
Most of Michigan will be similar. (Many of us consider it to be the most beautiful state) Southern Michigan, in particular, is excellent bicycling country. It rolls enough to be entertaining without working you to death. The difficulty will be with the roads, though. You'll find some roads that are just made for biking; good paved shoulders for instance. But many roads will be narrow with very fast motorists and blind dips and rises. Still, it's a good bicycle state on average.
If I thought about it, I could go on with other recommendations. But maybe that would take up too much space. You could choose almost anywhere east of the Mississippi River in autumn and do just fine, on average. Stay away from the mountainous areas, unless you want that sort of thing. September through early November is a good time in the North.. South of the Ohio River you might want to make it October through November and, perhaps, into early December.