After exiting the airport I took a cab through one of the pre-paid taxi stands there (there might be cheaper options but I didn't want to waste the limited time I had to explore). I exchanged the USD at the airport, although, in hindsight, I think I'd have gotten a better rate at the ATMs.
Me in Mexico City
The taxi dropped me about 2 blocks from the hotel, it cost about 305 Pesos (~22 USD). I had booked a hotel close to Zocalo which is their main square. Think of it like the heart of the city; thousands of people throng this square during weekends and special occasions. It's the thriving spot of culture, politics, and all major events happening in the city.
You'll find street performers, road side vendors, bargain gift shops, among others, at Zocalo. It also has the most important historic and architectural monuments of the city: The Metropolitan cathedral, National Palace (Palacio Nacional), Mueseo de bella arte, Palacio Postal, Angel de la independencia (the latter three are walk able distances away).
Best Time To Visit
Best time to visit Mexico City is from January to April