Don't worry too much about bottlenecks. Every system has bottlenecks. That's why no PC runs Crysis at 100000 fps. In technology you need to make choices. With a limited budget, you need to make choices.
With a faster videocard, you will always get faster frame/sec. But at some point, the CPU is doing so much work, the system can't get out frames any faster. While the GPU is still not 100% used. You might think you wasted your money. But there is more than just pure fps. There is eyecandy too (graphical feautures). When your CPU is 100% busy, and your GPU is not, just make your GPU work harder. You can do that by enabling more features. Configure higher settings in Skyrim. Install the HighRes texture pack (you'll have 2+ GB of videoram now). Enable better and more Anti-Aliasing. Maybe try SSAO. Etc, etc.
So suppose you have 30 fps average now. With a new videocard that is 3x faster, you should get 3x30 = 90 fps. But in reality, because of the CPU bottleneck, you get only 50 fps average. You might be disappointed. But then you enabled 4xMSAA + SMAA (for less temporal aliasing). And then 4x SGSS Transparency too (Sparse Grid). And your fps will stay at 50 fps. Then you install the high res texture packs, and your fps drops maybe from 50 fps to 48 fps. You set all settings to Ultra, and you stay at 48 fps. You enable SSAO (Ambient Occlusion -> better shadows) which will cost a lot of extra work. But your fps drop only from 48 fps to 45 fps. Result: you go from 30 fps to 45 fps. But at the same time, you will get a *lot* better image quality.
Buying a new/modern/expensive videocard just for higher framerates, but not for better image quality, is a waste of money.
I went from a E8500 + gtx260 to a E8500 + gtx680. Yes, my framerates went up, but not spectacular. But I could enable all the eyecandy I wanted, plus high res textures. My game looked 10x better ! Well worth the money, imho.
Then 2 months later I bought a i5-3570K. Perfect combination now. But if I had a limited budget, I'd buy a new videocard first. And worry about CPU (and mobo + RAM) later.
Hope this helps.