The ESPRIT-ARENA can be easily reached by public transport. From the hotel you just go down the street. After 10 minutes you reach the subway station `Stockumer Kirchstrasse`. (There is also a bus there, but it is hardly worth it)
The U-78 then takes you to Arena in 4 minutes.
If you do not want to go back to the hotel on the way back and want to make a stop in the city centre, you simply stay in the U-78 direction main station and go through to Heinrich-Heine-Allee ;-).
The best way to reach the ISS DOME is by taxi, with bus and train you would have to change twice, which we can not recommend.