Well if you decide to stay on 1680x1050 you can save on the gfx card; you won't need extra juice for full HD.
I'd get a third-generation Intel i5 - either a 3570K if you intent on overclocking or just a regular 3470. I'd get a B75 chipset mobo (they are cheap and support PCI Express 3.0), and a Radeon PCI-E 3.0 card like 7870 XT (a limited edition card with some of the 7900-series architecture but 7800-series pricing) or 7950. If you've got money for it, it's worth considering a Z77 motherboard for better overclocking ability, added features, SLI/Crossfire compatibility and so on. If you do that, you could also consider keeping your 560ti and pop in an extra one if you can get one cheap and you can be bothered fiddling with SLI and you have a PSU that can support two power-hungry cards simultaneously.
I got an i5-3470 and a Radeon 7950 and I play BF3 @ 60 fps in highest settings in full HD, and I paid less than 800 quid for my rig (including an ASUS 23-inch full HD screen) a couple of months back.
EDIT: Perhaps you should keep your card and just upgrade the rest of your rig and save the money for a gfx card in 6-12 months. PCI-E 3.0 is backwards compatible, so you shouldn't have a problem using your 560ti on a newer rig, and you'll have the option to upgrade to some super fast card for BF4 down the road if you get a chipset that supports PCI-E 3.0. According to this you should be able to pull an average of 58 fps in BF3 in your current resolution on high settings with your current card and a second-generation i5 (i5-2500).
Also take a look at this for CPU's (It's updated monthly like the one Trail linked below for GPU's):
