As to WHICH islands to include in a "week or so" before or after a RS tour ... the usual US choice is what I call "the Cliche twins" -- Santorini & Mykonos. Why?? Because people hear about them from friends who have taken 4-5 day cruises. The cruises only can stop at certain islands because those Gigantor Vessels require deep-water ports, which are very limited. So their brochures promote their ports as the "must-sees" And like lemmings, newcomers rush to them... and find themselves surrounded by thousands of Americans, and no Greek-isle authenticity. Do some real isles homework (i.e., a guidebook such as "Rough Guide" or EYEWITNESS: the Greek Isles), look at a map, and decide what would speak to YOU, not what is most "famous."
Nonetheless, most first-timers do gravitate toward the islands that have the poster-famous "sugar cube" white houses with blue shutters and red flowers, surrounded by beaches.... these are called the Cycladic Islands -- see location on this map http://www.greek-islands.us/map-greece/ and Santorini & Mykonos are among them. Most first-timers want to see at least one of them, and of the 2 I'd say SANTORINI. But realize that it's only 12 miles long, and its beaches are, well, a polite word is mediocre (in fact, black gravel-grit from volcanoes). So I'd say, 2 days (3 nights?) there, mainly for the caldera views ... and the rest of the time on a larger, more authentic Cycladic isle, with lovely beaches, dramatic inland scenery, mountain villages, ancient ruins ... Either NAXOS or PAROS -- and RS forum regulars will know I nominate Naxos. Here are great photo albums from one of my fellow Graecophiles, "stanbr" (who takes better pix than I do!), to start you off:
SANTORINI - https://www.flickr.com/photos/stanbr54/sets/72157632154800782/
NAXOS JUNE 14 - https://www.flickr.com/photos/stanbr54/sets/72157645113682278/
NAXOS - TRIP AROUND ISLE - http://www.flickr.com/photos/stanbr54/sets/72157634605629689/
... If u stay in Naxos, you get a "Bonus" -- it has dedicated excursion vessels that do day-trips to Mykonos & Delos or Paros, so you can get a taste of those isles & still get back to Naxos for sunset & dinner.
LOGISTICS - If you decide to do islands prior to an RS tour, Greece regulars have found ways to minimize transit. Ferries to Santorini take 9-10 hours: a flight takes 50 minutes. Plan well in advance & you can often find a "sale price" Aegean/Olympic flight to Santorini on the day of your arrival; just make sure to allow 2 hours layover-time to get thru passport control, pick up luggage, get €€ at ATMs & check in for domestic flight (it closes 45 mins before departure). After seeing Santorini, people enjoy taking the afternoon 3:15 BLUE STAR large ferry (1200-1800 passengers) to Naxos; you can sit on deck & see the caldera drama as u depart; it's 2+ hours to Naxos, a nice mini-cruise. From Naxos there's 1 flight per day, 45 mins (but a small plane so book FAR ahead), and also 2 daily Blue Star sailings to Piraeus, 5 hours but pleasant.