Despite of the young age of the city, the history of the settlement along the river "Wupper" goes back to 1161. "Elberfeld" was first mentioned in official documents as an estate of the archbishop of Cologne and received its town charter in 1610. "Barmen" was charted in 1808.
The "ICE" (Inter City Express, the German high-speed train) stops only at the Wuppertal Hauptbahnhof (HBF), the main station in Wuppertal. S-Bahn (Schnell-Bahn) and RE (Regional Express) trains stop at several train stations in Wuppertal, although the main station is probably the most convenient for most tourists.
An attraction in itself, the Wuppertaler Schwebebahn  is the world's oldest monorail system, dating back to 1901. The suspended trains run for 13.3 kilometers across the city in about 30 minutes, mostly above the surface of the river Wupper, and features in the movie Der Krieger und die Kaiserin (The Princess and the Warrior), which is set in and around Wuppertal. On special occasions, the original Kaiserwagen, used by Emperor Wilhelm II at the inauguration in 1900, is still used. Trains run every few minutes and single trip tickets are €2.20, VRR tickets accepted.
If you want to go shopping, then the Old Town or now center of Elberfeld will probably be the best place to go, since it offers the widest range of different stores in Wuppertal.
You definitely have to try the Wuppertaler Brauhaus-Fritten and Spare Ribs in the Wuppertaler Brauhaus. Tastes best with a cold beer.
Like most German cities, Wuppertal brews a local beer exclusive to the city. The Wupper Hell and the Wupper Dunkel can only be enjoyed in the Wuppertaler Brauhaus, a former swimming pool converted into a modern brewry in Barmen, close to the city center.
Wuppertal has - just like the most German cities do - a Jugendherberge (youth hostel). This is perhaps the cheapest place to stay. Most of the time a little breakfast is included in the price for staying overnight. However a reservation should be made in advance.
If you want to go out, then the Luisenviertel is probably a nice Place to go. The Luisenviertel is part of the Old Town of Elberfeld and hosts a wide range of nice cafes and some restaurants. The most famous one is Katzengold.