A few thoughts from a Clevelander:
It could snow and be cold all of April and early May here. Or it could be 80. Usually the 2nd half of May is decent enough, unless it's not. The weather forecast is inaccurate 90% of the time, the other 10% it's iffy.
US20 could be hairy as you head east out of Cleveland. I would just go east out of downtown via the North Marginal (by the Rock Hall) and head onto the bike lane, into Bratenahl, and then pick up OH-283. It's flat and has many miles of bike lane (there are a few dodgy stretches near Euclid and Willowick, but they are short). Smooth sailing until Painesville, where US-20 which becomes a 4-lane thoroughfare posted at 45mph (but driven at 65) with absolutely no shoulder. Unsafe at any time of day - but easy to get around. I can help, just drop a PM if you find this to be part of your travels.
PA is a mystery to me, but I would guess US20 is part of the equation, maybe PA-5 which eventually becomes NY-5. NY-5 from the PA line to Buffalo has an ample shoulder and is mostly flat save for some rollers. Lots of beautiful views, wine country, etc. From Buffalo, you can pick up the Empire State Trail and take that all the way to Albany.
As others have mentioned the Ohio To Erie Trail I'll say that it's a masterpiece and worth checking out if you have time and if it works with your route from Kansas, whatever that looks like. Cincinnati to Cleveland, 326 miles almost exclusively made up of bike trail - aside from 17 miles of rolling hills in Amish country, and some city/town riding. Plenty of hotels along the way as well as a few camping opportunities.