There are several good options in that range and they will give you much better gaming experience, assuming your CPU and other parts are decent.
I would consider:
GTX 750 Ti - it's on the outer limits of your budget, but is extremely low power and wouldn't require any additional PCI-e power plugs from your PSU.
R7 250x/R7 260 or R7 260x - Are good options too in this price range. If you have 1 x 6 pin PCI-e power connector on your PSU these will be good options too.
AMD 7770 Ghz edition - is last gen GPU, but still performs quite well and you might find some good prices on it, it will need a 6 pin PCI-e power connector from your PSU to run though, so keep that in mind.