Unfortunately you do have to travel quite some distance to find whitewater rafting trips near Las Vegas. Nearly all the rivers flow on the west side of the mountain ranges that stretch most of the length of California. So often times the issue is that the passes crossing the mountains are closed due to snow.
Accessible from from the southernmost pass via I-15 and Hwy 58 is the Kaweah River. This river is rated class 4+ (so not for the timid) and is about 5.75 hours west of Las Vegas, NV. See rafting near Three Rivers Below.
One of the rare rivers that flows due east from the mountains into Nevada is the East Fork Carson. Head north up Hwy 95 and come join us for 1-2 day wilderness trips located an hour south of Lake Tahoe. See rafting in Nevada below.
Since rafting in Southern California and Nevada is limited, you might have to take a little extra time and choose to travel to the Gold Country or Lake Tahoe area. Here there is a variety of rafting options for all levels available April-September. Also other recreation options, camping, numerous accommodations, wineries and other fun stuff!