Hi Nick,
Happy to add my two cents' worth to the valuable comments above. First, though, congratulations on choosing to visit & ride in Atlantic Canada, a beautiful place that has a special place in my heart. We sailed up the St Lawrence in late May 1956, emigrants from the UK. The Gaspé was my first view of Canada, and we disembarked at Lévis, across the river from Québec City. I was just a youngster -- I turned 9 a couple of months later -- but All That remains with me.
I've done a number of tours to and around Nova Scotia, New Brunswick, PEI and Québec, on my bikes, my motorcycle, and by car. You'll see the Newfoundland & Labrador is not yet on the list... (I had a 3-4 week tour planned for 2020, along the Gulf Coast of New Brunswick to mainland Nova Scotia and Cape Breton, but that Unseemly Bizness of COVID spiked that.) I've always camped, using hard accommodation only occasionally, usually when it's raining hard.
I'll draw on that experience in what follows.
From your post, I understand that terrain and lodging are the key issues for you and your wife. My overall suggestion, then, would be to:
(i) fly into Halifax and rent a car (van?); then
(ii) use that to tour Nova Scotia -- both the south and north Atlantic shores, as well as the Fundy Shore and Cape Breton. If you take your bikes along, you could stop at a motel at a small town -- let's say, Digby on the Fundy Shore, and make day rides east and west along the coast road. It's worth noting, though, that along much of the Fundy shore, there's a steep climb and drop between the secondary highway (#!) and the coastal road proper.
NS does have "undulations", but they're steep & demanding. Using a motorized vehicle would let you visit Cape Breton readily enough, and you could then use your bikes for shorter visits, e.g. to the French fortress of Louisbourg.
For route planning & following, I've used both Osmand and Komoot on my laptop & phone. The topographical feature is very useful. And, I also use large paper maps for planning -- e.g., Michelin.
PEI, as mentioned, has much gentler terrain for the most part, and is much easier cycling.
You might consider a cycling tour of (part of) the Gaspé. It's beautiful, and its own special place. You could take the train from Halifax to, say, Matapedia (at the Québec/New Brunswick border, at the head of the Baie de Chaleur.) From there, you could go eastwards along the south shore of the Gaspé, perhaps as far as the small town of Gaspé, and then take the train back west to Matapédia.
On VIA and bikes: I haven't taken my bike on a VIA train for a few years. In years past, they did provide a cardboard box free of charge. On one occasion, however, they shipped it a day ahead of my journey. (!! I'm not making this up.)
As for routes, I understand that VIA Rail has just reinstated the service along the south shore of the Gaspé, to the town of that name. (VIA's service is often, er, what the politicians call "aspirational"...)
If that Gaspé option seems of interest, it's a longer conversation -- let me know, and I can tell you more about my route.
On other matters: yes, August is a nice time to travel in those parts. Mind you, in my planning for my Ottawa-Halifax ride, I checked the NS Tourism Board's advice on weather in July/August. They said (about the Fundy Shore) something like, "Travellers can get 3-4 consecutive days of sunshine. That would be unusual, however."
As for bugs: Canajans have this weird thing about the wee bities, a kind of perverse boasting that "our bugs are bigger, meaner and hungrier than your bugs." Never understood it myself. But, here's Wade Hemsworth's ode to the blackfly:
https://www.youtube.com/watch?v=qjLBXb1kgMoBlackflies are
supposed to be done with by late June. But I always take a headnet with me when I'm in the woods in the summer; and when I'm walking, I used bug repellent with 30% DEET.
Other things: Halifax is well worth a visit in itself, especially the Citadel. It has seen its share of catastrophe, mind: the Halifax Harbour explosion of 1917, for example; and the bodies received from the
Titanic, as well. (Some are buried in Alma Cemetery -- the nomenclature of empire...)
Music rewards exploration. I'm very fond of the Rankin Family and the Barra Macneils. Many people like Rita Macneil and the Men of the Deeps. For fiddlers, I'm partial to Natalie McMaster; others prefer Ashley McIsaac.
For reading, check out short stories about Cape Breton by Alistair Macleod; or longer ones by Silver Donald Cameron.
Hope this is helpful, Nick. Good luck, and enjoy your planning!
John