Can someone post a better realistic budget for me?
Plan the budget around two paychecks ($2870/mo) and use the 'extra' paychecks to go STRAIGHT to you debt ($2870/year).
Your budget is tight because of your debt payments. I tried to infer your priorities from your comments (personal care and clothing are important) and attack other areas that you didn't seem as attached to (just from comments, so I might be off base). It's difficult to be a single person in an expensive area. Please don't take any of my recommendations as judgement. I understand how easy it is to fall into this cycle, and I admire your desire to get out. However, it isn't going to be easy or comfortable.
You mentioned that your car saves you $21 when you visit your family. However, you would need to visit your family 4 times per month to make the car a worthwhile investment. This is also ignoring any mileage devaluing from the driving (just based on your $75/mo estimate). I would recommend you sell your car, estimated value $1k, and pay off your cc with the $500 balance and put the other $500 toward your $3k card. I used to have an older car too, so I understand how a huge repair bill can pop up. Unfortunately your budget can't sustain even a minor repair. I also increased your 'other transportation' budget line to reflect a trip to visit your family.
Here is my take:
Rent: $850
Electric/Gas: $35
Subway pass: $120
Other transportation: $100 (an extra $20 added to reflect the loss of the car)
Professional fees/exams: $100
Drinks/dinner: $50
Coffee: $20
Haircuts/lady maintenance: $50 (Decreased a little bit)
Food: $200 (check out budgetbytes.com I'm obsessed with making the black bean quesadillas in bulk)
Clothes: $50 (Try to avoid shopping totally for a few months. Remember this isn't forever)
Gifts: $0 (Explain that you can't afford it right now)
Travel to weddings: $0 (Not in the cards for the next year)
Car: $0 (Breathe a sigh of relief b/c you won't have any big unexpected bills)
Before your debt repayments, the budget allows for $1475/mo spending. This is much lower than the average mustachian, and I understand it will be difficult. Realize this is temporary. Get out from under the debt gorilla as fast as possible to minimize the interest paid. This leaves 1395/month to attack your debts until September when it increases to $1687.
Minimums
CC: $250
SL: $484
With the sale of your car, you've already wiped out cc3 and part of cc2. With the remainder of the 1395 (after minimums), you should be able to pay off cc2 in about 3 months. After that, you'll be able to pay off cc1 in about 4 months. Then you can attack your student loan debt with the same method.
Good luck! After you pay down your debts, you're going to be insane in your savings. Your savings rate will put a lot of mustachians to shame!