Estate agents; Frank Salt, Alliance and Remax Malta. I'd recommend renting before deciding to buy as it could be a culture shock. I also recommend hiring a car or using taxis to get around, even though it's a small island getting around on buses is slow, difficult and can be crowded... Also Maltese people don't believe in queuing.
Gozo is quieter and less expensive than Malta, it has lots of retirees. There is a high speed catamaran ferry from Valletta to Gozo that is very good... But I would think being older they may want to live on Malta so they are closer to Mater Dei hospital, it depends on their health really.
If you go to the channel 4 app you can search for 'A Place in the Sun' episodes there's about one episode per season set in Malta or Gozo.
Maltese people will see your parents as tourists and take every opportunity to charge them extra for anything and everything so they should be prepared to stick up for themselves/negotiate and learn a little bit of Maltese. If they don't negotiate they'll likely be seen as easy marks... Especially if they have American accents. And Maltese property prices are silly high. Maltese people can't afford to get on the property ladder so people are trying to get as much money as they can from "foreigners". That being said there is very very little crime in Malta, it's a very safe place.
On Malta Marsascala is probably a good place to start looking as it's got a nice feel, is by the water but isn't as busy as Sliema and St Julian's. If they aren't fussed about being close to the water maybe try the Rabat and Mdina area, it's got excellent views as it's on the high ground in the centre so you can look out across the island to the sea.
There is a Baptist church that I've forgotten the name of (sorry) that has American ministers, they offer to collect people from their accommodation and drive them to church... They might be worth contacting for a bit of 'on the ground' information for new expats.
Also look in YouTube there are videos of retirees and digital nomads living in Gozo.
HTH