If you and your travel companions are looking for accommodation in Saransk, it may be helpful to be aware that Expedia's booking site of hotels in Russia doesn't currently include accommodations in or near Saransk itself.
Approximately 380 miles from Saransk is Volgograd, which has a number of hotel and apartment options, such as the Yuzhniy Hotel and Hampton by Hilton Volgograd Profsoyuznaya.
Why not investigate the many delights of Volga while you are in the area? Explore Volga's traditional villages and old towns. Those with a hankering for fresh air and wide open spaces should also make the time to admire its forests. Travelers in this section of Russia enjoy skiing, cross-country skiing and hiking.
Expedia's travel guide is an excellent way to learn more about Saransk.