This is an excellent urban cycling path - well built and maintained, and flat the entire way so it's an easy ride. The bike path runs along the top of the flood levy on the south bank of the Lanyang River. On one side you have a view of the Luoyang suburbs (mostly rice paddies and farm houses), and on the other side is the flood plain beside the river. Because the typhoons wash down rich topsoil from the mountains every year, the fertile flood plain is farmed after typhoon season ends. If you ride from fall to spring, you can watch the farmers tending their crops.
The bike path is pretty long, so you can start wherever you want. Riding the entire length and back takes about 2 1/2 hours. It runs from the mouth of the Lanyang River up to the foothills. Halfway along the route you pass by the Luodong Sports Park, which is a big popular park with many recreational facilities. You might want to make a detour and take a look. At the point where the bike path dead ends upstream, it's an easy ride along a local road to get to Meihua Lake (see my post), which is worth a visit. To get to Meihua Lake, ride upstream until the path comes to an end at a traffic roundabout. Cross the roundabout (be careful! - roundabouts are bad news for cyclists) and take the road going downhill. After a couple of minutes you will see a brown sign pointing the way to the lake. Turn right and follow this road to the lake. There are some shops along this road selling snacks in case you're hungry or thirsty.
One great thing about this bike path is its central location. It connects with several other bike paths, so from here you can get to quite a few places. If you cross over to the north bank of the river at the Qingzhou Bridge 清洲橋, you can get on the Annong River Bike Path 安農溪自行車道, which you can ride as far as Sanxing 三星,which is popular with Taiwanese tourists. Near the mouth of the Lanyang River, you can cross over to the north side and get on the Coastal Bike Path (see my post), which I highly recommend. Or, near the mouth of the Lanyang River you can turn right and follow the little local roads south to get on the short southern Coastal Bike Path, or else the Dongshan River Bike Path 冬山河自行車道 which runs through Dongshan River Park next to the Center for Traditional Performing Arts. You can also easily get to several smaller bike paths from here, or else explore the surrounding neighborhoods.
If you don't have a bike, you can rent one at Meihua Lake. To get to the river from the lake, just take the road away from the lake and turn left at the first corner. Follow this road uphill for a few minutes to the traffic roundabout. On the other side is the beginning of the Lanyang River Bike Path.
One problem with this bike path is that there's almost no shade - you're exposed to the sun almost the entire way. On a summer day, it will be a really hot ride. Be sure to put on sunscreen, wear a hat, and drink plenty of water.