A great park to go to is called Bon Echo. It is reletivley close to Algonquin, my family used to go to it every summer when I was younger. If you have amall kids it is a great park. If you don't there is also another park attached to it called Joe Parry, these sites you have to canoe to (you can rent the canoes) but they are nicer and and they are all right on the water so you can swim right out of your site. It is a great place to bring animals. Even though you seem to be be alone you are never more then a 25min drive away from a general store, and 45min outside of a small town. As far as walking trails, Bon Echo is situated at the bottom of a cliff on the edge of the Canadian Shield. There are great paths that go up the cliff, they are all easy and built for families. In the main park there is also a wonderful beach that is just great for swimming. Thier site is
http://www.ontarioparks.com/bone.html, I hope you have a good time wherever you go. You can also go to ontarioparks.com to get info on all the parks.
Michael