The historic town of Neuwied has traces of existence going back well in time. The architecture in the inner town shows signs of a Gothic era. The inner town is often referred to as the old town.
Once consisting of a generally poor demographic, the town has made drastic changes in the past 100+ years. To learn the most about the history and culture I highly recommend the bicycle guided tours. This allows you to see what someone is trying to explain. There are bus tours available, too, and many of the local attractions offer the same.
If you are limited to a day trip to Neuwied, you will only be disappointed that you could not stay longer. There are numerous castles, a wonderful zoo, and even a museum of archeology of the glacial age.
With a lot to offer, you may want to plan your sights ahead of time. There can be a lot of wasted time spent on trying to figure out what to do or where to go. This will also allow you to make sure the attractions you are interested in will available.
The indoor pool facility of Deichwelle is great if you are traveling with kids, and you run into bad weather. Another option is Piratenland, an indoor pirate adventure park. Recently added is an outdoor playland including a giant waterslide. You can have lunch in the restaurant while taking in the atmosphere, and watching the younger kids go crazy. ;-)
The variety museums offer pretty much something for everyone. There is a pinball museum, which consists of antique pinball machines and related items. There is also an art and culture museum located near the train station. The Kreismuseum is the regional museum of Neuwied.
The Deichinformationszenturm (what a long word, huh?) is the tourist information center and holds its own exhibits as well. With much to see and do, you will not have a moment of boredom.