I had to go to the US Embassy in July. Other than the Micro Hotel(didn't get very good reviews on Trip Advisor) and the AirBnB's mentioned above, there's really not much close to the Embassy. Pretty tacky area - kind of run-down and somewhat industrialized. You really have to go south of JFK Expressway(Hwy 1)to find any hotels.
I just renewed my passport on Monday. *I stayed at the Posada Delia del Alba. It costs 36 US (1700 pesos) and is about a 10 to 15 minute walk to the embassy. Its closer than the Micro Suites that costs 3000 pesos. It's not really a hotel. You get a bedroom with 2 beds and a private bathroom with a shared living room and kitchen. I found it online and called the owner who was very nice. She recommended a taxi driver who picked me up at Metro for 250 pesos. I wouldn't recommend it other than for going to the embassy since there are no restaurants or grocery stores close. Especially if you don't have a car.*
My recommendation would be to get the earliest appointment. They are at 7, 7:30 and 8 AM. They let you enter even if you are early. The sooner you get there the sooner you will get out. Once you go through the scanners, you take a number and go upstairs and wait for your number to be called. They only call out the numbers and announcements in Spanish but the people who take your information all speak English. They take your 110 US in dollars, pesos or credit card and they do have change. You pay after you submit your paperwork and then go back outside the embassy to stand in line at Domex courier. That's 16 dollars or the equivalent in pesos. They also have change. I heard them tell the person in front of me that they didn't take credit cards.*
One more thing. Even though there are no signs warning you, no cell phones or WiFi devices are allowed inside !!! You go through a line just like at the airport and are scanned.