Hi Paul,
Algonquin Provincial Park has a couple of good weekend-long backpacking routes, and tons of paddling routes. The backpacking routes all feel quite different even though they're relatively close together. There's a great interactive map:
http://www.algonquinmap.com/
Frontenac Provincial Park is pretty good for an easy overnighter or short weekend. The paddling routes are pretty well travelled but I've hiked there a few times and never seen anyone else on the trails. It's a good bet for a holiday weekend as there's much less traffic getting out of the city in that direction.
Bon Echo has a short backpacking trail and lots of paddling.
There's also the wilderness section of the Ganaraska trail. I haven't been on it, but I've heard good stuff.
Bruce Trail has a couple of backcountry sites up by Tobermory: High Dump and Stormhaven. The Bruce Peninsula is spectacular, and doesn't get many blackflies — makes for a good may/june hike when the rest of Ontario is intolerable.
Killarney is a bit far for a weekend, but well worth it if you have more time.
Ontario has an interactive crown land atlas online:
http://www.ontario.ca/environment-and-energy/crown-land-use-policy-atlas
Canadian Canoe Routes has a good database of paddling routes in ontario:
http://www.myccr.com/canoedb/on.htm