What is a realistic astronaut mission for today?

How about there is this satellite which needs repair.
Or a space station that needs repair.

If you want Sci-Fi you can do a comet came near earth and they sent astronaut to collect samples/study/blahblah(you can fill that up).

I hope that works.

Perhaps he has gone to check if the satillite is picking up the right data. And if it isn't, he could go and fix it or something!
Or an abandoned item is found floating through space, and he has to go and check it out. It could just be a part of a rocket.
Hope this helps!

Most astronaut missions in the present travel to and from the International Space Station (via the Shuttle or other vehicles like the Russian Soyuz).  These missions sometimes bring new sections of the ISS to install.  Some astronauts remain on the ISS for months at a time, doing experiments.  Other manned missions involve work on orbiting satellites.

If you're wanting to write a story in space, you could have one of these missions be the setting, but since it's become a bit routine, you might want to consider making it a near-future setting, involving NASA's new plans to return to the Moon.

Space station, as visiting crew for example. Maximum of 14 days. Training as visiting crew is generally task based and not skill based, so the visiting crew will be quite busy in these 14 days doing the experiments they have trained for on Earth.

Satellite service missions are still possible (For example STS-125), but are not economic.

Another pretty disliked job is capsule jockey for a rich space tourist.

Finally, the lunar missions will first only take a few weeks, before becoming longer stays.

how about this, the earth has run out of its fossil fuels and things are getting to be real tough. nasa sends a manned space craft to Triton ( one of jupiters moons) which is covered in natural gas. the astronauts mission is to do some recon work and somehow get that natural gas onto the space craft for scientific purposes. they have to defeat all odds and see if humankind can get through this race to save our Earth.