To hitch through the Greater Cleveland Area (Cleveland-Akron-Canton) you will prefer to avoid the metropolitan centers and move, as much as possible, through more suburban ones. The best roads should be the long non-highways connecting important towns. Those on the highways have too little room to stop to risk picking you up, and drivers on short, residential roads will be few, uncooperative, and simply unable to take you any distance. Police tend to be unsympathetic. You can use the website of the Greater Cleveland Regional Transit Authority to figure out public transit options to get to a good starting point from anywhere in the city. Buses cost $2.25, and you need exact change.
East on 322 towards Pensylvania
Get to Mayfield road, and take a bus to the last stop. Mayfield road turns into US Route 322. Walk about two kilometres, past a hospital and a church and along a long stretch of road with no traffic lights. The first traffic light you come across will be a good spot to hitch from. Benny hitched from Cleveland to New York using this spot and got a ride within three minutes. He didn't use a sign and found that just asking drivers to roll down their windows and asking them if they could take him East worked very well. He mostly got short rides (20-50 miles at a time) until he got to Pennsylvania. From there it's a matter of taking the local roads (Route 6 goes all the way to the East Coast, but it is extremely rural and goes through a forest) or turning South on one of the many junctions to get to I-80.