I assume you'll have a car. "Near" Century City is, I s'pose relative, as Century City itself is mainly office towers. That said, the whole West LA area is primo eating zone.
Pretty much my favorite tag-team of LA eating is right by Century City. That would be Falafal King and Stan's Donuts. I love Falafal King pretty much for their daily selection of 20 odd salads and dips, their multiple hot sauces and the gratis chips. Whatever your "real" order, it is mostly superfulous to the sides. Then on to Stans, perhaps the greatest of LA donuts (meaning the greatest donuts in the world). Falafal King is at 1059 Broxton Ave in Westwood. Stan's is around the corner at Weyburn.
As to Mexican food, Guelaguetza is an Oaxacan place much different than anything in Chicago. All sorts of items from the Oaxacan kitchen like clayudas--like a big tostada or pizza and memelas, like a sope, and delicious hot chocolate, and well way more than you can order in one outing--and I've tried. There is a branch at 1127 Palms (off of Sepulvada), which is not to far from Cen City.
LA has so much great food, but perhaps my favorite meals there are the most "normal". Nothing is more normal and more better than the french toast at DuPars, a few locations, but the only one close to you will be the Farmer's Market at 3rd and Fairfax.
If you have more spefic questions, let me know.
Rob
PS
I wanted to add, that near by Century City, on Sawtelle is a heavily Japanese section. I do not know specific places, but it is my understanding that there are great places in this zone. And another highly rated donut place (which I only tried at the end of their day), Primo's is on Sawtelle.