I think Cap-aux-Meules (Grindstone) is the only place where you can rent moped's. CAA is probably the best place since it is fairly close to the harbour, but there are probably other places too.
Entry Island is a good walking area. It has gravel roads and little traffic. There is a restaurant/cafe, a little museum (English), lighthouse, Big Hill (tallest on the islands), etc.
La Grave and La Cote (Havre-Aubert and Etang-du-Nord harbours) have a lot of little shops that are great for looking into the Acadian culture. Site d'autre fois is interesting with a miniature village and life size structures depicting what life was like in the past. It is always good to know how things evolved.
La Salicorne (Grande-Entree) gives walking/kayaking/biking tours plus other interesting activities.
Mines Seleine gives tours now too and has it's own eco-museum. It gives ideas on how the islands came into existence as well as the mining of salt. The Hydro power plant also gives tours explaining the history of power to the islands and the process of getting the power to where it is needed here on the islands. There is a little fishing museum in Grindstone also..., off hand I can't remember the name of it.
There are a couple of self-guided tours of the East Point Wildlife Reserve which end up on the big beach. And there is Brion Island Ecological Reserve but you need a guide to go into the provincial side of the reserve. Still the Canada side is a good days worth of walking, lol.