A small group of us will be staying near Taiyuan and would like to take a day trip to the great wall, any suggestions?

You may take high speed trains from Taiyuan to Beijing first. It takes about 3.5 hours and costs 152 RMB for second class and 217 RMB for first class. When you arrive, you may take No.83 bus to Deshengmen. There you can take No.919 or 877 to visit Badaling section.

Is there no way to go from Taiyuan to the Wall directly? Do we have to go back to Beijing first?

For Badaling section, no direct bus or train is available from Taiyuan.