Have an Answer?
Really honest statement and good question!
Much of the EE arena has become program related even to design digital circuits where one writes a description for the logic in a language like C++.
I was a BSEE with a focus on analog. Analog is still needed as analog is the interface between the CPU (using digital and programming...) and the real world which is analog! So if you like to tinker go look up some opamp circuits (by the way you can build some yourself like audio amplifiers..) and see if you like tinkering with analog circuits.
If you want to be "hands on" with PCB design using analog circuits you could get a BSEE with focus on analog or you could bet a BSET (engineering technology) and be a technician which involves a bunch of tinkering. Other area which require hardware tinkering is product engineering where you work on yield enhancement and fixing things when they break in manufacturing.
I was a Audio/Video guy before college so it was easy for me to go analog. However as you know most things go digital so you still need to understand digital side a bit even if you focu son analog.
Hope this helps and respond if you want to know more cheers Peter