Beth -- Your text is somewhat confusing; I've been to greece many times, out of Philly and NY, and still my head is spinning. To clarify, I believe what you're saying is that you want us to recommend the best choice for your parents arrival/departure -- and you will work your own flight plans to adapt to that choice. Is that right?? In paragraph 2 & 3, you're talking about your own fligfhts, but in Concluding, you ask us to help you choose flights for your parents. Which?? Also, are your parents coming from Ft. Lauderdale as well? Or somewhere else? Here are some observations, based on 12 Athens trips, nonstops and Europe connections, and also with/without a 2nd connection to an Island-bound flight:
PHILADELHIA
• American (exUSAir) Nonstop 4:30pm - 9:15 AM next AM is 100% on-time arrival in ATH... also shortest actual airtime of any line. But of course, seats uncomfortable, food bad, fares higher.
NEWARK
* Haven't used; do you ask about 2hr40min layover between arrival from Ft Laud and outbound flight to Athens? Or layover upon return? For you on May 20, Or parents on May 26? Both?
HEATHROW
• United (or other) flight with Heathrow connection --- in my experience, Heathrow is nerve-wracking even if you have 3 hours between flights. Why? It's world's busiest airport, & Does NOT assign gates ahead of time!! Those changing planes must go to big central Pen and stare at huge boards for their gate number. It finally pops up, it says "boarding at _" (30 minutes)... and it takes 20+ minutes to reach the gate!!! IF you don't lose your way!! You run down loooong concourse, avoiding wrong turns, down escalator, out of exit door onto bus, off bus onto rail platform, then MUST exit car at correct Station (1-2-3-4) to find gate. Nightmare. I do not recall (trying to repress the memory!) whether you must go thru security before admittance to Central Pen. I think so. I was in my 60s, fit and energetic, I Ran down that concourse. How old/fit are your parents?
VIENNA
• I've never connected there, but this link describes a new terminal that makes connection easier -- https://www.austrian.com/Info/Flying/Terminal.aspx?sclang=en&cc=AT -- multi-level terminal with escalators: to go from one airline's gates to another's, people need only change levels, not sprint or bus between different terminals ... that's something I would certainly welcome!
CONNECTIONS in GENERAL
ATHENS AIRPORT
• In Late May, tourism traffic is already getting heavy, but it depends a LOT on arrival date; If arriving on Saturday or Sunday, expect bigger crowds; Also, fewer flights between 9 - 12 am; after that, Many connection flights from Europe and other Continents flood in, crowds multiply.
• A time-saving plus: Athens has only ONE terminal. Once u get thru passport control, you can grab bags & quickly reach either the street, or domestic flight check-in line. In my May trips, deplaning at 9:30 am, thru passport line, bag pick-up, ATM visit = 45-50 minutes. Afternoon time = 1hr 20.
ON-TIME AVERAGES
• Nonstops - Any day of week, no matter how delayed departure may be from PHL, JFK or Newark, even if more than an hour late, these arrive ATH on schedule -- they have all that ocean time to make up for delays.
• Europe Connections - There's where delay factor builds in. If you arrive Heathrow 7 AM for 9 AM take-off for 3 hr flight, you lose 1 hr, land ATH 1pm .. probably 15-20 minutes late. Later in day, connecting flight departures from Rome, Frankfort, etc etc are 12 or 1, liklier to be delayed , as well as longer lines in ATH airport.
I hope my experience can help you sort out choices ... and please do clarify who you are asking for, so that others may respond helpfully.