It might matter what your current CPU is. Since you're talking about only upgrading the CPU, I imagine that you have an AMD CPU now, probably a Ryzen 1x00 or 2x00? If it's 1x00, I'm not sure, but that might bottleneck a 3080 and prevent you from getting your $699 worth out of it. In that case, a lesser GPU model + a CPU upgrade might make more sense.
The way that I, personally, look at it is that you could spend $400+200=$600 to have last year's GPU (2080 Ti) and last year's CPU (Ryzen 3x00) now or wait a few months and get a Ryzen 5x00 and either an RX 6x00XT or RTX 3070 for not much more just so that you can feel good that you have the latest hardware and know that it'll likely last you an extra year or two. The gaming performance would likely be similar in either case, so are greater pride and peace of mind worth waiting for? That's totally for you to decide. For myself, I've decided to wait, save up and treat myself to AMD's latest CPU and GPU later this year or early next year, but that's just me. I've, unfortunately, gotten very used to having outdated hardware (not just one generation, but several generations old) and would like to have something new for once, but that's just me. I've waited so long that I can wait a few months more. I can appreciate that not everyone might want to wait, though.