The Bruce Trail runs from Niagara up to the Bruce Peninsula, but it is entirely west of Toronto. It connects most of the small, interesting parks in the area (denoted by * below), many of which I have been to and visit regularly.
I'm not sure how far out of the city you can get, but these are some smaller, day-trip parks I've been to all within two hours' drive...
Silver Creek Conservation Area* Forested hiking trails Free road parking on Fallbrook Trail and Side Road 27
Terra Cotta Conservation Area* Forested and marshland hiking trails Parking lot (can't remember if paid or free) off Winston Churchill Blvd
Limehouse Conservation Area* Forested hiking, low cliffs, crevices, caves, remnants of an old lime mill Free parking lot off 5th Line. Might be busy with baseball teams (two diamonds adjacent)
Kelso Conservation Area* Been a long time since I was here Cliffs, ski hill, forested hiking trails Parking lot, likely paid, off Tremaine Rd
Rattlesnake Point Conservation Area* High cliffs, climbing hotspot, some forested hiking trails Paid parking lot off Appleby Line
Mt Nemo Conservation Area* High Cliffs, crevices, forested hiking Paid parking lot off Guelph Line
Borer's Falls Conservation Area* Cliff, waterfall, forested hiking Paid parking lot off Rock Chapel Rd
Dundas Valley Conservation Area* Large park with wide trail network Mostly forested hiking, maybe some cliffs and crevices Parking lot, likely paid, off Old Dundas Rd
Mono Cliffs Provincial Park* Boardwalks, crevices, cliffs, marshland and forested hiking Parking lot (can remember if paid or free) off 3rd Line E
Nottawasaga Bluffs Conservation Area* Crevices, cliffs, forested hiking Been awhile, would assume road parking on Sideroad 15 & 16 Nottawasaga
Nottawasaga Lookout Provincial Reserve* Cliffs, crevices, forested hiking trails We've always accessed from road parking at the corner of Eagle Cres/Osprey Clearview Townline
There are many more (and many more just on the Bruce Trail), so it may be beneficial to have a look around, especially to the east of the city where I am not as familiar.
If you can push out to 3-ish hours you can get to:
Arrowhead Provincial Park Silent Lake Provincial Park Kawartha Lakes Provincial Park (Canoe-centric) Oxtongue River Ragged Falls Provincial Park (smaller park w/ swimming amongst rapids) Algonquin Provincial Park Queen Elizabeth II Wildlands Provincial Park (on the Ganaraska Trail)
The latter two are bigger parks where I get away for easy weekend backpacking trips. Algonquin will require day permits, but QEW is 'non-operating' and is free if you know how to access it (Devil's Lake Rd off Deep Bay Rd in the east, or Black River Rd in the west. The southern access near Sadowa/Morton is closed due to land dispute, I believe.)
If you want to stay relatively urban (I don't recommend staying on any of these after dark):
Don River & Massey Creek Trail System in Toronto Forested trails the follow the river systems. Busy on nice summer days. Free parking lot at Taylor Creek Park off Don Mills Rd and beneath the DVP This parking lot used to have a reputation as a meating spot on Friday nights...
Colonel Samuel Smith Park Medium-sized urban park on the city's waterfront. Nice view of downtown (CN Tower) to the east. Great place for birding with swans, fowl, and various other migratory and non-migratory birds. There's probably paid or free parking lots at the car entrance, but I always parked on any of the nearby numbered streets between Morrison St and Lake Shore Dr to the east of the park and then walked in from the Lake Shore entrance (not to be confused with Lake Shore Boulevard)
Bruce Trail through Hamilton* Follows the Niagara Escarpment through the middle of Hamilton. From about Devils Punchbowl in the east to Scenic Drive in the west will offer nice hiking. The two ends mentioned will be busy on summer days (west more so than east). Parking can be found at various points along the trail, mostly road parking, mostly free. Punchbowl can be accessed from a paid lot on the escarpment (Ridge Rd) or below (street parking, Mountain Ave S). There is turn-out road parking off Scenic Dr.