To do a video card upgrade a power supply upgrade is required. The low end of the mid range cards that I've seen all require at least 400W, and true they might not use it all but something tells me that PSU is not of a brand that would be trusted to actually do well at its rating.
I'm running an Athlon II X2 250 (3ghz) in my desktop and it's definitely lacking for Crysis 2 and Skyrim. You're better off upgrading to a quad-core (try Phenom II X4 975 or AMD FX series) with atleast 3.4ghz/core... not necessarily because it will run Skyrim or Crysis 2 better, but because it future-proofs your system a little more.
Quad-core and beyond gaming is just around the corner I believe.
Odd, Skyrim runs fine with the Athlon 64 6000+ dual core 3 Ghz and GTS 450 1GB. Are you sure it's your CPU limiting Skyrim?
I do agree a Phenom II X4 is a good idea for a new computer though. I get the Phenom II X4 965 (3.4Ghz) for $115 last month. I know it can be overclocked, but I'm not voiding my warranty and increasing power usage for a CPU boost I don't even need. This machine has the GTX 460 1GB card but I list the 450 above because I know it can run Skyrim fine.