There are a few good shops in Provo/Orem. Mad Dog Cycles is on 800 S, just east of State St. in Orem. They also havea shop in Provo. Timpanogos Cyclery is in Pleasant Grove, and also a good bike shop. If you want to go further South, Springville has Blayn's Cycling Service on Main St at about 300 South.
As for trails, there are a few. The Bonneville Shoreline Trail has connections in Orem and Provo. There is also the Provo Canyon Race loop behind Mt. Timpanogos Park in Provo Canyon. It's a short, easier loop which is pretty fun. There is also the Provo River Pkwy. Trail which runs from about 6 miles up the canyon at Vivian Park all the way to Provo River. It's total of about 13 miles. There are several up Payson Canyon and American Fork Canyon if your looking to drive a litte bit out of town. Good luck and have fun!