I make that and live at 25th / 3rd in a studio ($2,200 /month).
When you enjoy your apt you go out less (on weeknights anyway) so I value that a lot.
You can then spend $300 /week on random crap and still put $1,500+ towards savings, loans, etc.
If you want to spend less on rent you can have 2-3 roommates and pay $1,200-1,600 for a bedroom nearly anywhere in the city.
For fun the East Village is great. I can cab it there for $5-6 or walk there in 20 mins.