I sold a 720BE / HD4670 to a friend and his teenaged son around a year ago. The son bought Skyrim recently, and according to the Dad, it has been running quite well; I think at 1280x1024. The GTS240 is a stronger GPU, and the i7 860 is a dramatically better CPU, so I think the OP's rig will run the game pretty well. Try it as is before spending money on upgrades. If the experience is unsatisfying, then decide how best to improve it.
Edit: ...although I do agree that, in general, a larger monitor will be an improvement for EVERYTHING for which that PC might conceivably be used. How well the rig runs now however may suggest how much stronger the graphics card should be for a larger monitor, so test first.