Let me first say that East Liverpool itself is not exactly ... ummmm ... charming. Unless you're into the run-down industrial look. However, the rest of that northern tip of West Virginia, western Pennsylvania, and eastern Ohio are quite lovely ... green and hilly.
The bridge at Newell is definitely a toll bridge and I'm not sure how they would feel about a bicycle crossing, but the one near Chester is not ... that's the BIG bridge Rowan mentions above. And you do have to have your wits about you when you cross that one. If you cross from East Liverpool into West Virginia, and continue straight up Hwy 30, you'll be going up for quite a while ... there's a good sized hill climbing out of the river valley! I'm not sure about the bridge at Steubenville.
I'm also not sure if cycling is allowed on the Ohio side, but it definitely is on the West Virginia side. If you decide to ride on the West Virginia side, I'd recommend travelling up Hwy 8 to New Manchester (I believe). There is a little brown, wood-panelled grocery store there, at the top of a hill, which had some amazingly inexpensive prices on groceries! We went back twice!
I'd also recommend Racoon Creek Park/Campground near Frankfort Springs in Pennsylvania. It's a very nice campground in a beautiful park ... but one tip .... if you do decide to camp there, be sure you've got some very secure storage for your food!! It isn't named "Racoon
" Creek for nothing!!
By the time night fell, we were surrounded by little glowing eyes shining out of the heads of very bold masked bandits!