It would be helpful to know what CPU you are using, the model number, as well as model number of your memory. Memory with tall heat sinks can cause clearance issues with some CPU coolers.
Are you prepared to possibly remove the mother board to install the new CPU cooler? The cut out on the mother board tray of the case may not allow access to the screws and mounting back plate of a new cooler. You can check that easily by removing one side panel of the case.
Did you build the PC yourself? Have you ever mounted a cooler before? Your budget for this cooler?
A popular and above average CPU cooler that is not expensive is the Cooler Master Hyper 212: COOLER MASTER Hyper 212 EVO RR-212E-20PK-R2 Continuous Direct Contact 120mm Sleeve CPU Cooler Compatible with latest Intel 2011/1366/1155 and AMD FM1/FM2/AM3+ - Newegg.com
That cooler is just one example, there are others that would be work well and fit on your board an in your PC. The 212 will fit since it can be positioned with its long dimension either vertically or horizontally.