To cost you $30 a month you would need to be drawing 300W 24 hours a day. I really doubt that, what do you use the PC for that uses so much power? I have a 6700K and a GTX 980, power costs me $0.25 a KWH, I use my PC a lot, and it doesn't cost me as much as you say, more like $10-$20 on average. If you really want to find out costs invest in a watt meter and measure it, there is no other way to actually know and they can be had cheap enough.
Also a modern graphics card when idling or not being used for demanding tasks does not use much power regardless of what it might use at full load. Compare the idle power consumption of a mid range card with a high end one and you'll see there is not that much difference if there is any at all.
The only time the power consumption will be higher is when you are gaming or using the graphics hardware at high load, unless you do that for a significant part of every day it's unlikely a graphics card upgrade will make more than a few dollars a month difference to he power bill if that.
So basically what I'm saying is get whatever graphics card you want and the extra power costs aren't likely to be much. If you really believe it will cost you much maybe a 750ti is the best choice, it's still the fastest card that doesn't require an extra power connector I believe.
Or maybe a better way to approach it, go here
http://outervision.com/power-supply-calculator and put in your system specs. then just change the graphics card and recalculate. that'll show you the difference in maximum power draw and give you the worst case. Bear in mind most of the time PC's don't use maximum power.
By doing that I see a 960 uses up to 40W less than a 560Ti and a 7950 uses up to 20W less, so both are a saving and there's 20w between them. If you managed to run your graphics card at 100% load for 24 hours a day 40W will save you $4 and 20W will save you $2. I really wouldn't worry about the power consumption.