Itinerary Advice: Belgium, Italy, Czech Republic, Hungary, Greece

Why do you want to fly after stopover in Iceland to Brussels? I know, that's one of few cities where Iceland Air flies directly from Reykjavik (Keflavik) but Zurich is closer to Italy (Munich, too). And you can connect to Italy by train. Then you would fly to Prague, fly or train to Budapest, fly to Athens. You are also mentioning Barcelona but then you say you are not interested in Spain. Well, Barcelona is in Spain. Your itinerary in part 1 makes sense. About part 2 I don't know because you have no interest in Paris and although you are mentioning Barcelona you are not interested in Spain.

Hey Ilja,

Thank you for your response!

I was flying into Brussels because I found a cheap fare through WOW Airlines, which has a stopover program. However, I see your point of flying straight to Iceland, and then flying with Iceland Air to a hub closer to Italy.

I may edit my itinerary to be Brussels > Paris > Northern Italy.

OK, I can see that you already eliminated Barcelona. If there is Iceland Air direct flight from Reykjavik to Paris, take it. If not then there is a good fast connection by train between Brussels and Paris. From Paris to Italy either fly or train. And then it will go the same as you already have it.
Edit: I just wrote this answer before I saw your second post. So my advice is the same as you already decided.

Thank you Ilja, your advice is really helping me make some final decisions! I see that it's really come down to deciding between Brussels and Paris. The city of Paris I've been to, but I can leave my traveling companion to see the touristy items of Paris and take day trips alone to places like to Versailles and Rouen. Now my questions left for anyone else are these:

1) What I'm missing out on by not going to Brussels?
2) What city makes sense to fly out of?

Well, it's not Brussels you're missing, but Antwerp, Gent, and Brugge. Why wouldn't you fly out of Athens? It's peak season and island airplanes might be hard to book. I personally wouldn't spend so much time in motion, but it's your trip. Greece will be sweltering.

Question 1: what you are missing: not much. Some boulevards in Brussels resemble somewhat Paris but of course Paris is original and better. Flowery Main Square is interesting. Lot of beggars around train station. Famous statue of peeing boy. Oversized modern buildings of the capital of European Union. It must have taken a lot of money to build it and obviously it contains a lot of space to accommodate too many bureaucrats.
Question 2: where to fly from back to US. If you are not tied to certain airline (like Iceland Air) then Athens. Otherwise one more plane change to get to the Iceland Air hub city like Copenhagen, Brussels, Amsterdam, Zurich, Munich and some others which I don't remember. So in that case: Athens - hub city - Reykjavik - your city in US.

We would usually visit Pisa for a half-day on the way to Florence (staying 3 nights there), rather than sleeping in Pisa with additional hotel check-in.

Nailed down my itinerary.

Fly into Paris, with stopover in Iceland through WOW Airlines. (2 nights)
Paris (3 nights)
Italy -
Lake Como (2 nights)
Cinque Terre (2 nights)
Pisa + Florence (3 nights)
Prague (3 nights)
Budapest (3 nights)
Greece (8-9 nights) - Athens + Island Hopping between Mykonos, Santorini, possibly Hydra
Fly out of: Athens > Paris (hub) > DC

Total cross-atlantic flight cost: $600 + ~$200 for ATH to Paris hub connection.

Remaining Decision:
Turns out I'm short a day or two, so I'm trying to figure out what to cut from the following out of Italy:
Lake Como
Cinque Terre
Pisa
Tuscany countryside

I've already been to Florence and Rome, but those might stay on for my traveling companion.

I'd cut Pisa, but that doesn't really buy you much since it's usually just a 2-hour or so stop. I like the Italian lakes a lot, but that's a good bit of traveling for what would be not much more than a day in the area. I tend to think of the lakes as a place to take it easy for a few days.

I'm confused. You said Greece, Hungary and Czech Republic? Then you throw in a bunch of other stops? Fly to Greece, then either Ryan or Wizz has discount flights to Budapest, then train to Prague.