The majority of tourists who visit Riobamba do so to take the train to Alausí and ride through the famed Devil’s Nose. For this reason, the majority of places to stay are concentrated around the train station. If you are on a budget, and will only be in town for a short while, there are a number of cheap hostels. They may not have as many amenities as a fancy hotel, but for one night, they tend to do the trick.
If you are planning on staying in town for a few days, and have a larger budget, and are looking for a quiet holiday, it is worth staying at one of the hotels that are located outside of the city of Riobamba. They tend to be fancier, and the scenery is unforgettable.