That's a tough price to get much closer to Manhattan. Stick with Queens neighborhoods - you'll be equally closer to your work, but in a better quality neighborhood compared to your Brooklyn options at that price. Astoria would be my choice, even if it's just to move closer and see what it's like - the N should get you to work in about an hour.

But, be aware that you may be more comfortable in a different situation than me, so you might enjoy a rougher neighborhood or an older apartment in Brooklyn as a trade-off for living within a certain distance from work.