Honestly, I'm not that interested in learning about FPGA's and arduinos. I'm more of a hardware guy.
FPGAs are hardware! The difference is that instead of wire-wrap, you write lines of code that describe the hardware. At every instance, you are thinking about how hardware works. You will use gates and D-flops to build anything you want.
My personal view is that, with wire-wrap, I am limited to projects of 100 ICs or less. No, that's not a hard number but at some point, wire-wrap becomes a PITA!
It's pretty easy, and fairly cheap, to get an FPGA board with a device of well over 1 MILLION gates. And they run pretty fast depending on the circuit design. 50 MHz is easy, 100 MHz might take a little more thought (and pipelining). Some devices are MUCH faster.
My own interests lie in analog computing and FPGAs. I have designed and built a functional equivalent of a 1960s minicomputer that runs the factory software unchanged. It took quite a while to learn how to write VHDL (and arguably I still don't know) but it was fun bringing the machine to life. A computer that took up a large desk is now reduced to the size of a postage stamp. With room left over...
Robotics is fun! There's a lot going on with the added computing power of boards like the Raspberry PI. We are finally getting to the point where we can do computer vision and WiFi allows the robot to offload some processing onto bigger, but stationary, computers.
CNC machines are still being built from parts and pieces. It's pretty handy to have a CNC mill for making front panels and such.
Op amps are fun! I tend to play with analog integrators since my interest is in analog computing but there are dozens of other applications. In college, we waved our hands at the equations defining damped harmonic motion. With an analog computer it is possible to visualize the interaction between mass, spring rate and damping coefficient. I truly wish I had had an analog computer while I was in college. This was pre-<just about everything> so, at best, we had HP-35 calculators and a slide rule. Today, Matlab does a pretty slick job of emulating an analog control system. I wasn't one of the students with the HP-35. Bummer...
Audio is a large segment of the hobby community. It isn't something I care about but I will toss it out as a possibility.
Then there is amateur radio. Another area where I don't have any interest but there are thousand and thousands who do. I'm not sure how many of today's amateurs are building there equipment. When I dabbled with the stuff in the late '50s and early '60s, almost everything was home-built.
Microcontrollers! Beyond the Arduino, there are some interesting projects being built with the modern ARM processors. It's not all code because, sooner or later, the uC has to talk to the world.
So, there's a partial shopping list. Good luck!