The problem with a platform upgrade is, you're going to drop $250+ on a Skylake CPU (and you probably won't see a ton of improvement unless you go for an i7, which is even more expensive), and then you're talking $150+ for a motherboard and you'll also need all new RAM, so Skylake will easily run $400-500+, depending on the CPU, motherboard and RAM you choose.
If you're otherwise happy, I'd recommend a GPU upgrade. I found out the hard way that VRAM can cripple you, and 1GB simply won't be enough for many modern titles at 1080p. I ran GeFroce 570s' in SLI in.... 2011? And they performed admirably, until about early 2013 when the 1.25GB (or whatever they had) of VRAM forced me into an upgrade. If you want something to last a while, a 380 with 4+ GB VRAM would be fine.