I have 150$ to spend.
I will be getting a 6870 or maybe a 6850oc. Either of these will be by more than enough to run Skyrim on very high for 150$.
i have an nvidia 9800 gt right now and it actually does a very impressive job at medium high on skyrim atm.
So like the first guy say, it may not be your Graphics card thats your problem atm.
It might be your CPU. both have to hit a certian point.
Search Youtube for "8800gs skyrim" to see how others are doing with your current card.
Then search youtube for the 6870 skyrim, or which ever other cards your interested in.
Your CPU is probably just as much of the problem, perhaps more even.
If you have 124$ to spend on a CPU and 50$ for a mobo, check out. Great CPU for the price. Newegg.com - AMD Phenom II X4 960T Zosma 3.0GHz Socket AM3 95W Quad-Core Desktop Processor HD96ZTWFGRBOX
If you have 150 to spend on a CPU check out the AMD 970 or fx 6100.
both very great chips also.
Though if you change chips, of coarse then you need a new mobo, and have to make sure your ram and hard drive and power supply will still work.
If all you can afford is a graphics card (Its a safe place to start) but you will probably end up needing both to see a difference.