I think there is software program called HADES, it provide good and clear simulation for MIPS with its other versions; single cycle, pipeline, etc.

I'll make one self-answer here, just in case someone else wonders about the same software for similar purposes.

MARS simulator for MIPS architecture is a very nice and simple tool with a clean and intuitive GUI.

It is a Java app (JAR), so it can be run everywhere as long as adequate JRE is installed.

Any other suggestions and possibly better solutions are very welcome.

@Ghada: I will look up this HADES software.

You can check this

http://tams-www.informatik.uni-hamburg.de/applets/hades/webdemos/index.html

Very useful for running programs is SPIM

http://pages.cs.wisc.edu/~larus/spim.html

It contains an assembler, also some IO and interrupt facility.

Programs can be run in single step mode, showing all register content etc.

It is described in the appendix of "Computer Organization and Design"

We used this in the intro-course regularly and with good success.

I am not sure but you can take a look here:

http://www.altera.com/devices/processor/mips/mp32/proc-mp32.html

So this is several years late...

I wrote a MIPS/ARM/Nios II simulator intended for education use. It runs inside a web browser (avoiding installation problems), has a built-in debugger, and models I/O devices and interrupts. The MIPS mode is somewhat MARS/SPIM-compatible. The Nios and ARM modes have been used at the University of Toronto (and a few others) for a few years already, while MIPS was added January 2018.

https://cpulator.01xz.net/