I grew up there (now in Vancouver BC), and it can definitely be a frugal place, but the summer / tourist type activities tend to be more pricey. The National Park beaches (Cavendish, Brackley, Stanhope) have admission fees, which may be worth it for you, but there are also lots of other beaches that are great for swimming/going with kids/etc.... Check out Argyle Shore or Tea Hill (South Shore)or Blooming Point (North Shore). Thunder Cover and Cabot Park (where the LMM tv show Emily of New Moon was filmed) near Kensington are also good and free. If you like the LMM show Road to Avonlea, the hotel Dalvay by the Sea near Cavendish was used as a location.
As for Anne activities, the AGG house is in Cavendish and has a fee, but I don't think it's much. You can also walk through the trails on the property. LMM's grave site is free to access and is in a nearby graveyard.
Charlottetown has lots of great activities in the summer, and depending when you go, you could see the Fathers of Confederation actors, the Anne Musical at the Confederation Centre of the Arts, grab a beer (gahan house mentioned above is good) or coffee at one of the cafes along Victoria Row (right next to confederation centre). I would also suggest checking out some of the independent restaurants in downtown, as there are many to choose from. If you like Lebanese food, I would recommend Cedar's Eatery.
If you have a bike, there is the Confederation Trail that goes tip to tip, or just driving the island's country roads is very fun.
let me know if you have other questions!