Orange and East Cleveland, if you're talking about the city of East Cleveland (this is what Clevelanders mean by "East Cleveland"), aren't that close. If you're going to spend several days in East Cleveland then several days in Orange, I would suggest you relocate during your stay.
Probably the best place to stay near East Cleveland is the Glidden House Inn in University Circle. University Circle is adjacent to East Cleveland, but a much nicer area. From University Circle, you could drive west to East 55th, where a short drive south would take you to I-490, which would very quickly connect you to I-77.
If you're going to be going back and forth between East Cleveland and Orange, or if you mean that you'll be working in the eastern suburbs of Greater Cleveland, and not East Cleveland, check out the hotels in Beachwood:
The Marriott Cleveland East in Warrensville Heights, just off I-271 on Harvard Road, is extremely well located for Orange and is a little further south than the other hotels off Chagrin Blvd. in Beachwood.
If you want to stay further south, closer to Akron, check out hotels in Richfield or Hudson, depending upon where in the Akron area you plan to spend most of your time.
Enjoy your stay in Northeast Ohio!
Edited: 11:39 am, November 15, 2010