actually there are many places are within reach from Dusseldorf. as mentioned, u can take the RE to those big/medium/small town, but make sure you skip the S-Bahn (unless u have lots of time) because it will stop at all the village/town.
1. dusseldorf - you can walk along the ruhr river. there are some interesting buildings at one side (i forgot left or right side) of the river designed by renown architect (sorry i forgot many places it was roughly 3yrs since i last stayed there)
2. koln - but it's not under NRW region anymore so the ticket might be slight expensive compared to NRW (north-rhein westphalia) region. there are lots of english speaking people in koln. things there are also more expensive.
3. ratingen - espirit factory outlet! super cheap
4. oberhausen - zoo. maybe u can meet paul the octopus too
5. wuppertal - zoo.
6. essen & duisburg (nice old town), bochum (with underground mining museum), gelsenkirchen (a lot of turkish community here)
(i stayed in essen previously. if take RE to dusseldorf, roughly 30mins. if take s-bahn, roughly 1+hrs).
but basically, there are many old churches around. too bad i dont have dlsr when i studied there.