One popular place to visit near Vang Vieng is the Tham Poukham cave and the Blue lagoon next to the cave. Both places are located around 11km east of Vang Vieng. The road passing the bridge acorss the river in town is not paved, so while you could hire a bicycle it might not be the most comfortable ride. You could go there with a motorbike, or just go there by songthaew. The journey should take between 20 and 30 minutes.
The short ride is already worth the journey alone, heading out ot the rural area, passing fields, little village, strreams, crossing some dodgy looking bridges, kids waving at you shouting Sabaidee, while in the distance you can see stunning limestone karst in the distance. Stopping on the way for pictures or to enjoy the scenery is highly recommend.