We stayed in a B and B. Their are many and because the island is small location is not too important. Ours was $85 CA a night, we had our own bathroom and had the most lovely breakfast every morning( and with a 16% percent meal tax on all the meals we ate out this was well appreciated). We were free to come and go as we pleased and it was one of the best hotel stays of my life. Our innkeepers moved and the new owners are just going to live there so I can't recommend the exact place we stayed but try Windsong Farm B and B, They had been my first choice but were full. It is a charming old house and will help you get the feel of the island. Have a fun trip this was one of the best vacations We have taken.

Small world; my cousins both worked at this place when they were teens; the B&B is located near land my uncle owns!
OP; since you said you're only staying 2 nights, you probably want a fairly central, "accessible to the highlights", location.
Windsong Farm is located in Brackley Beach, which in my opinion is perfect. This B&B is located approximately equal driving time from Charlottetown and Cavendish (~20 minutes to each). If you want a motel instead, the
North Winds is a good place. There is lots of space for kids to play, or to just walk around. There's also a beautiful National Park beach nearby, and I don't believe they charge admission the time of year you'll be there (it will be too cold for swimming, but perfect for a nice beach walk!)

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Rodd Brudenell River is a gorgeous location, if you do end up staying there. It's not as close to the "highlights" parts of the Island as the other places I mentioned, but keep in mind that driving times between cities/towns/villages are relatively short in PEI. As a comparision, driving around the perimeter of the island takes 4-5 hours, so having to drive an hour from your hotel to see the Anne of Green Gables House might not seem so bad

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Feel free to PM me if you have any other questions; I worked in Visitor Information for 4 years in PEI, and practically my entire extended family still lives there. We go over to our cottage there several times a year; the time of year you are visiting is going to be beautiful

. Have a great trip!