Where are good and likely places in Ontario for one night backpacking only trips?
I dont have a full understanding of backpacking. I think of backpacking as a form of low cost travel where you get to experience the local culture and make some new friends and learn new things. Because I am not a big backpacker myself, I am afraid I cannot offer a great answer to your question.
However, I must tell you that you should check out couchsurfing and meetup.com. These are great community websites where you can connect with a group of like minded folks and plan trips and stuff. I have couchsurfed in Lithuania and it was an amazing experience. I am not sure how good it is in Canada, but its worth a try. Check it out.
Destination wise, I can suggest you some backpacking worthy destinations close to Toronto. Here they are:
1) Bruce Peninsula National Park and Tobermory – a great weekend destination about 4 hrs drive from Toronto.
2) Prince Edward County – a small island, famous for wine yards, farms, bed & breafasts. The island also has a popular provincial park called Sandbanks Provincial Park and is famous for its shallow fresh water beach.
3) And then there is Algonquin – one of the most popular outdoor destination in all of Ontario. There are a lot of hiking trails and camping sites to explore.
Frontenac Provincial park or Kawartha Highlands are great for short backpacking trips (weekend stays).
Eastern pines and highland trails in Algonquin park, Abes and Essens trail in Bon echo, several loop trails in Frontenac, Rideau Trail and Trans Canada trail, as well as Kawartha highlands all have great backpacking trails that can be done as overnight trips.