Your cpu may bottleneck the graphics card. I suggest the R9 270. This will be able to play all games at high with your cpu (with a more modern cpu it will be able to run games at ultra). You can also overclock this to give you better performance.
ATI Radeon HD 7790 and Nvidia GTX 650Ti Boost are the two good Graphic cards that fits in your budget but after installing them, your system will need 500W PSU.
Which PSU do you have ?
if you dont want to buy a new PSU then HD 7770 is enough for your system.
you can play latest games on medium-high settings at medium resolution with playable framerates.
Any card you buy around $200 will basically keep you CPU limited (i.e. it'll be your processor, not your video card keeping games from running faster). That said, I would recommend AMD R9-270. It's $180, is essentially an AMD 7870 for $20-50 less, and beats anything nVidia has for a similar price. It'll let you play pretty much any modern game on high-ultra at 1080p if you get a better CPU at some point.
Next significant step up would be a GTX 760, but you're looking at $260 or more which is way over your budget. The R9-270X (note the X at the end) is essentially a slightly faster (probably overclocked) 270.
Another card you can go for is the AMD 7850 if you can get it for $150. It's slightly slower than the 270, but still more than enough for games. Finally, there's the nVidia GTX 650 Ti, it's significantly slower than the 7850 and at ~$130, only $20 less but there are a bunch of bundles on Newegg with lots of free games.
tl;dr: Get the AMD R9-270. Edit: however, most of my suggestions need a 500W power supply, so a 650 Ti Boost is probably your best bet.
But does your Power supply have any PCIe power connection for these GPUs ?
if you're using any Cheap PSU then you should better upgrade your PSU and get a GTX650Ti boost.
Your cpu will handle this card nicely and your PC will be safe.
You can use Corsair VS450.
good and cheap PSU.