Rhodes has been on my “list” so I started planning for next July (2018). Was originally thinking 2 weeks or a bit more and hopping to a few other islands but as I researched I kept bringing up "package tours crowded", "nuisance to get to", "not especially interesting". I had decided on Rhodes with day trips to Symi and Chalki and then a few days on Kos. The ‘Pro’ is flights in/out of both Rhodes and Kos. But the ‘cons’ are it sounds like in July it really might be just too crammed with ‘package’ tourists. A recent thread asking about Rhodes brought up several links that were really discouraging. In a few years I’ll be able to travel in April/Sept/Oct. Would Rhodes be better seen in those months?

Assuming the answer to that question is yes, then I’m thinking some Cyclades islands (which I understand are NOT especially good off season – more chance of poor weathers, limited ferry schedules, etc.). From answers to some other threads I’m now looking at Sikinos, Folegandros, Milos, Sifnos and Serifos. Looks like if I want to fly in/out of the islands I’d have to fly in/out of Santorini?

Thoughts?

July is High Season for tourism in Greece so an island like Rhodes will be heavily crowded and more expensive just like most other Greek Islands, especially "Big Name" Islands.

Off-season is the best time to go to Greece and even Big Name Islands will be more tolerable to visit with the lesser known Islands a joy to be on.

The Cyclades are the typical Greek Islands most people think of so many of them will have crowds during July but if you pick an island like Sifnos you may have a better time than an island like Santorini but that is open to debate as far as what you are looking for. Regardless Summer Time will find most islands and many areas of the mainland filled with tourists plus the summer heat can be unbearable unless you like baking on a beach!

If you can hold off travel to Greece either during the Spring or early Fall you'll probably have a better time with less tourists, lower prices and still good weather.

Obviously some people can only take holiday during the summer and if so you should do more research to try and find an island(s) or parts of the mainland that don't get the heavy tourism like other parts of Greece do.

Santorini can get to either by plane or ferry with a flight a lot quicker than spending hours on a ferry but prices could be very high for High Season.

More research will be needed to find what you are looking for.

You are virtually completely wrong on every point.
Rhodes is a large island and is quite developed for tourism, however that does not mean everywhere is "crowded with package tourists" there some smaller places that are not very developed.
The only places you may find crowded on Rhodes are certain streets in Rhodes old town and Lindos. This in the main is due to Cruise ship passengers and daytrippers from elsewhere on Rhodes.

Nearby Chalki and Symi are niche markets for the UK. It's daytrippers from Rhodes that cause the daytime crowding not those who stay on these islands.

Nowhere on Kos is particularly crowded, cruise ships are relatively rare and small in number.

I have island hopped all the way up to Samos several times and have stayed a number of times on Chalki and Symi and many times on Kos.

"Assuming the answer to that question is yes"
It is a no, because you have it all wrong, very wrong.

Needless to say you have the comparison wrong with the Cyclades. The ferries there are somewhat better than going up the Dodekanese islands to Samos.

"Looks like if I want to fly in/out of the islands I’d have to fly in/out of Santorini? "
Again completely wrong. For the Cyclades you have named you would start with regular ferry route Piraeus > Serifos > Sifnos > Folegandros > Sikinos. You may pass thru Santorini but it is not pivotal.

Rhodes: most package tourists stay around
Kallithea - Faliraki - Kolymbia
Lindos
Kiotari
The main streets (only these!) within the walled city of Rhodes look crowdy in the evening, but not the small streets you have to walk through in ordr to go to good restaurants.

If you want to discover the Island by public bus and do some day trip to neigbouring Islands, the (stratecical) best place to stay would Hotel Hermes, in a quiet quarter, close to bus station, excursion boats pier and taxi rank. More scenic places (a bit farther away) within the north western part of the walled city (like hotel Attiki).

Some samll paces with no mass tourism, but nice sandy beaches:
Stegna, Haraki

The neighbouring Islands of Symi and Tilos can be visited in day trips (daily resp twice weekly), but it's much nicer to stay there for a few days.

As to Serifos - Sifnos - Milos - Folegandros - Sikinos: there are direct slow ferries and catamarans to/from Piraeus (port of Athens). At several days, it's easier to reach Sikons via Naxos (all by ferries).

You'll find lots of tourists on many islands in high season, so choose whichever one appeals and hope for the best! Rhodes Old Town was packed to the rafters when we visited one July, but so was Santorini, Mykonos, and Naxos.

As stated above, if you choose less popular islands, you'll probably encounter fewer tourists, but it could still be busy.

If it helps, I've found one of the best times for a visit with less tourists is end of May/early June. Never been in September, but after our visit this past summer in July, that seems like a great option for next time!