Hello again, everyone! I want to thank all of you for taking the time to reply and share your thoughts and suggestions with me. Over the past two weeks I have worked off and on to try and put together a more solid plan for this trip based on the suggestions that I have received, and it has been immensely helpful! I do not have too many updates yet, as my partner and I are both indecisive people, and I need him to give me places he wants to see and things he wants to do to further steer the direction of the trip 
The LAX airport in Los Angeles almost always has the cheapest flights in and out of southern California; however, so I did not even think to look at flying out of San Diego when we first started thinking about this trip. After deciding to look deeper into my options after the suggestions of trying to find a flight direct to Central Europe, I was shocked to find even cheaper flights from San Diego to Amsterdam and Frankfurt than from LA to Paris and London! They are not direct flights, like the flights to Paris or London are; however, the layovers are minimal without being stress-inducingly short, and they will deliver us to a much more central homebase for the trip and cut travel time, overall. This alone should help to make the trip feel less rushed as we still try and narrow down the scope of the trip and what we want to see with our limited time -- that said, I am currently trying to work with my employer to have a portion of this trip be classified as a work trip in order to save my personal time and potentially extend our stay another four or five days!
With that, itineraries most similar to what @amur leopard and @lintworm have suggested, or perhaps a combination of the two, are most likely at this point depending on what we decide to prioritize and where we end up flying in and out of. I do know that my partner wants to rent a car for at least some of the trip, as he is a bit of a transportation nerd and wishes to both experience driving in another country as well as public transport, so hopefully that will give us more flexibility. For me, now, in addition to the Berlins, Prague and Vienna seem like obvious choice, with Antwerp, Artis, Burgers, Cologne, Innsbruck, Leipzig, Nuremberg, Planckendael, Plzen, and Stuttgart all on the short list as notable options to potentially fill in the gaps with?
The LAX airport in Los Angeles almost always has the cheapest flights in and out of southern California; however, so I did not even think to look at flying out of San Diego when we first started thinking about this trip. After deciding to look deeper into my options after the suggestions of trying to find a flight direct to Central Europe, I was shocked to find even cheaper flights from San Diego to Amsterdam and Frankfurt than from LA to Paris and London! They are not direct flights, like the flights to Paris or London are; however, the layovers are minimal without being stress-inducingly short, and they will deliver us to a much more central homebase for the trip and cut travel time, overall. This alone should help to make the trip feel less rushed as we still try and narrow down the scope of the trip and what we want to see with our limited time -- that said, I am currently trying to work with my employer to have a portion of this trip be classified as a work trip in order to save my personal time and potentially extend our stay another four or five days!
With that, itineraries most similar to what @amur leopard and @lintworm have suggested, or perhaps a combination of the two, are most likely at this point depending on what we decide to prioritize and where we end up flying in and out of. I do know that my partner wants to rent a car for at least some of the trip, as he is a bit of a transportation nerd and wishes to both experience driving in another country as well as public transport, so hopefully that will give us more flexibility. For me, now, in addition to the Berlins, Prague and Vienna seem like obvious choice, with Antwerp, Artis, Burgers, Cologne, Innsbruck, Leipzig, Nuremberg, Planckendael, Plzen, and Stuttgart all on the short list as notable options to potentially fill in the gaps with?