The most popular times to visit Germany are the summer months and the winter holidays. The Rhine River's castles are picturesque in the snow. However, since so many of the activities in the area are outdoors, the summer is probably the best time to go. Try scheduling your visit between May and September, when the whether will be warm. You will encounter fewer tourists if you visit in May, as the high tourist season kicks into gear in June.
The Rhine is renowned for its romantic beauty. Medieval castles line the river and many of them are open for tourists to visit. The 35-mile section of the river between Mainz and Bonn is lined with more castles than any other section of river in the world. Burg Rheinfels, near the town of St. Goar, is one of the most famous. The castle was built in 1245, but in 1797, the French Revolutionary Army left it in ruins. The most well-preserved medieval castle along the Rhine is Marksburg castle, located next to the village of Spay.
Another can't-miss sight is the Loreley. The Loreley is a 450-foot rock that looks out over the Rhine. In ancient days, sailors claimed that a nymph lived on top of the rock and sang out over the river, enchanting sailors and causing them to wreck their ships on the nearby reefs.
The Rhine River Valley also has a variety of interesting cities and towns. Cologne is famous for its soaring Gothic cathedral, and there are other interesting medieval churches scattered throughout the city. It is the fourth-largest city in Germany, and has an excellent selection of restaurants along with a thriving nightlife. Bonn is a smaller city, but is no less interesting. Beethoven was born here, and you can visit his birthplace. The Old Bonn Cemetery is also particularly beautiful.
For small-town charm, the town of Bacharach is a great place to stop for a night, with some of the finest vineyards in the Rhine region. Koblenz and Mainz are popular places to stay for a night simply because they bookend the most scenic and romantic section of the river.
The closest airport is Flughafen Frankfurt-am-Main in Frankfurt. From there, you can take a train to Cologne. Stop in Cologne and see the sites, or head straight on to Koblenz if you prefer. There are trains on both sides of the river, and the view out of your window is guaranteed to be amazing.
If you are not prone to seasickness, you can also see the Rhine via boat. Cruises are available that take you past all of the major points of interest along the river. If you don't mind getting some exercise, the Rheinsteig trail runs along the river for 200 miles. You can also rent bikes, and there is a bike path on the west side of the river that runs 35 miles from Koblenz to Bingen. Of course, you can also rent a car. However, traffic may be heavy, especially during high tourist season.