Apart from the weekly Saturday market, there are not many reasons for stopping at Riobamba during a trip to Ecuador. Place Maldonado in the centre of town has a beautiful cathedral and some colonial buildings with lovely facades. Other than that there's not a lot else to do there.
In fact, stopping in Riobamba is really only interesting because of its surroundings. The scenery is superb. I really recommend going to Chimborazo park. There are walks up the volcano's 6,310 metres that are accessible to everyone. Other than that, you could enjoy going round one of the town's markets. But either way there's no reason to linger in Riobamba.
For me, the main attraction of Riobamba – which is located four hours from Quito and lies at an altitude of 2,750 metres – was the fact that the city is the departure point for a train that once descended all the way down to Guayaquil, at sea level. The line has now been alarmingly reduced in length. However, and being stubbornly determined to experience it anyway, an Equadorean friend and I caught a bus to Alausí (a two and a half hour journey) and did in the end get to experience the most spectacular part of the route, culminating in the "La Nariz del Diablo" (The Devil's Nose), with its 360° bends, from the roof of the train.
The line begins 1,000 metres higher than it ends and you have the constant feeling the train is going to derail at every turn. If you like trains and intense sensations, this really is something to experience, even though it would definitely have been more interesting to be able to travel the whole length of the line, from Quito to Guayaquil. But that was another era!