Growing up between New York and Boston, I was used to subway/metro systems being rather dirty and terrible. However, when I first entered Moscow's, I was completely blown away. As well as being several stories underground, the stations were completely spotless, decorated with chandeliers, murals, and statues, and incredibly efficient. Every station was unique in its own way, with different designs and decorations (most commemorating some part of Russian culture or history), and since there are 14 lines with 20-30 stops each, the sheer magnitude is mind-blowing.
One day, a few friends and I decided to make an adventure/photo project out of it by traveling to some of the most interesting and elaborate stations throughout the city and taking pictures of what we saw. Even though I knew it would be interesting, at the very least, it ended up becoming one of the best activities I've done since moving there. We went during a weekday in the evening, after rush hour, so there weren't too many people around, therefore giving us the ability to see much of what is missed during the standard commute.
I couldn't recommend this enough. By doing a self-constructed metro tour, you can see all the subtleties that went into creating and engineering the whole underground system. I advise seeing as many stations as you can, but as for some recommendations, make sure to see Комсомолская/Komsomolskaya, Маяковская/Mayakovskaya, Пло́щадь Револю́ции/Ploshad Revolutsiy, Киевская/Kievskaya, Белопусская/Beloruskaya, Арбатская/Arbatskaya and Проспект Мира/Prospeky Mira among others.