The railroad tracks going through the five towns kind of divide the steep from the flat and not so steep. On the water side. the streets from the tracks down to the water have some incline/decline and some level parts. But, as I recall, they are not bad at all. Monterosso has an old town and a new town and the walks between them are not bad. Above the tracks, there are some level areas close in but within a few hundred feet, the streets begin to rise. Some streets can be a bit steep. There is good news here. Each town has mini-bus service. I don't think that they go between the towns but they do go up and down the hills. If you have a Cinque Terre Treno card, it's free.
Anticipating your next question, yes there is a CT Card. It's called the Cinque Terre Treno card. They come in 1,2,3 and 7-day flavors and can be purchased at TI offices in the CT. The pass provides unlimited free rides on the train from Levanto in the North to La Spezia in the south. Further it covers the fares on the coastal trails (yes there are fare booths on the trails). You can easily walk the first trail from Riomaggiore to Manarola. It's level. You might be able to walk the second trail from Manarola to the Corniglia train station. There is one area with a small hill and there are 4-5 dozen stairs at the end as you descend to the train station. We're seniors and we did it quite easily. Finally, the card is good on the mini-buses and for the local museum. It's not good on the ferries.