Thinking of a CPU upgrade.

A CPU upgrade might help, but not enough to make it worth it. Are you seeing full usage on all cores while in game?

Adding RAM will not give you better performance.

I am guessing that since you have an HP it is unlikely that you will have any unlocked features for overclocking. OEM PC's rarely have any OCing options.
 
Well what FPS are you getting with Skyrim and at what settings? I don't have a lot of experience with the game but I can tell you what to look for.

In general, AA and AF is really tough on GPUs so turning that down to 2x, 4x or off might let you jump a level (Medium -> High)

Check what your usages are. In game, Alt + Tab and see what your CPU, GPU and RAM are running at. Your GPU should be at 100% or at least close. If your CPU is at 100% then you have a bottleneck. Same with your RAM.

Post back your findings and I can help you figure the rest out.
 
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