I was already planning a family vacation to Europe (Paris + Italy) and an opportunity for a business trip to Rhodes came up, so trying to see how best to combine the two.

What other destinations in Europe can be paired with Rhodes, Greece for a 15-day Europe itinerary in June? We would like to explore 3-4 major destinations, preferably in different countries. We like history, architecture, food, beaches etc. Not interested in strenuous activities like hiking, scuba diving, climbing too many steps (few are okay) or visiting too many museums (a couple of major ones okay) etc.

I was considering Paris - Rome - Athens - Rhodes but wondering if-
1. Will this be too much travel and too expensive?
2. Is there a different route that gives us a glimpse of Europe but is not as hectic/expensive?
3. If we increase the duration from two weeks to three weeks, that will also bump up the expenses quite a bit, right? Anyway, we are open to 15–20-day trip that is within a reasonable budget.
4. Between Italy and Greece, which is better for someone on their first Europe trip?

Any special reason you chose Rhodes? I liked Rhodes, but it is an unusual choice for a first trip. I would consider Athens - Crete - Rhodes - Istanbul, but Italy would be a more "normal" choice than Greece. Not that I think that should necessarily influence you.

Edited above - it's a work trip to Rhodes. I was already planning a family vacation to Europe (Paris + Italy) and this work opportunity came up, so trying to see how best to combine the two

adding one more question
5. Should we skip Athens altogether and do US-Paris-Rome-Rhodes-Paris-US? (based on some Youtube videos I watched that say tourists skip Athens and just do the Islands). The reason I have Paris at start and end is because we fly Delta and Paris is most convenient to fly in/out of. I saw there are direct flights between Rome-Rhodes & Paris-Rhodes.

It is usually a mistake to backtrack to your starting point - a waste of time and money. Use the multi-city option on sites like skyscanner and kayak.

I found plenty to do in Athens. In addition to the must-see Acropolis there are several worth-while museums.

Travelling to four or five places, in different countries, in 15 days is too many. In 15 days you could do 3 places. Don't forget you will lose most of a whole day when you travel from one place to the next. Out of Paris, Rome, Athens and Rhodes I'd skip Athens but that's just my opinion. Lots of people love Athens. You need to look at what there is to see and do in each place (start with Fodors but Trip Advisor is helpful too) and decide what will suit you the most.

Saying if something is too expensive is impossible. What's expensive to one person might be cheap to another. If you increase the trip to three weeks, you have the extra cost of accommodation, transport and food. Airfares may stay the same, depending on what you include in your trip.

If you're coming from the US your biggest cost is the flight to Europe. Adding a week means more for hotels and food but the same flight cost from the US.

June from Rome your flight options to Rhodes are limited. That's something to check.

The best destination is the one that interests you.

Please don't let people dissuade you from spending time in Athens. I, too, heard that "get out of Athens asap" nonsense and, after 2 visits to Greece in the past 4 years, I couldn't disagree more. I very much enjoy the islands, but Athens is awesome - and quite budget friendly.

I would visit the Dodecanese Islands after or before Rhodes.
The Turkish coast is lovely so consider visiting some of the towns there like Bodrum, Fethiye, etc.

How long will you be on Rhodes for your work trip? That’s going to eat into the time for your family vacation unless you can extend your trip in Europe. There are non-stop flights from Rome to several Greek islands in high season, but otherwise you will have to go through Athens to get to/from Rhodes. For someone interested in history, it would be a shame to be in Greece but miss Athens.

Rhodes pairs well with Kastellorizo (aka Megisti), and Bodrum in Turkey.

Bodrum is a popular beach resort. Istanbul would be an incredible option if you like history and culture and can endure the crush of the crowds.