The "something unusual" part of your request is the tricky part. Spring migration can bring things but it can whisk them away too.
I hope you already use
http://ebird.org/ebird/map/ ?
If so, you'll know it's a great way to check for recent sightings at various parks.
Two things I'd mention in the West side of the GTA:
IF you haven't seen a pair of nesting Red Necked Grebes, and IF you want to, and IF they nest there again this year (although they've been very reliable) there's usually a pair nesting in the Bronte Marina about 6 feet from shore/the main pedestrian path on a manmade platform covered in sticks and weeds. Not perfect for photography in the a.m. because the light is the wrong direction, but very nice to see and reasonable photos. It may be a bit early for them, so it would be worth checking eBird or posting again here and asking if anyone has been out to see them.
Bronte Marina is very easy to get to. You take the 427 south to the Gardiner and out west along the QEW, or
you take the 403 west to the QEW
then you exit the westbound QEW at Bronte Road, and go straight south to where it ends at the Lake. The road curves along to the left becoming Ontario St and there's a large yellowish building with the Compass Restaurant in it and huge free parking lot/children's playground etc. The birds nest just a tiny bit east of the restaurant in this tiny channel of water beside where the boats moor. Very not wild! [google map "Bronte Outer Harbour Marina, Ontario Street, Oakville, ON" will show where it is.]
Don't take the 407: the toll is huge and most rental cars charge a ridiculous surcharge.
Other common birds at Bronte Marina include barn swallows (in the bandshell roof) and cliff swallows (on the sides of the restaurant), and the usual terns and gulls but not usually any rarities.
The other park if you do go to Bronte Marina is back north up Bronte Road to immediately north of the Queen Elizabeth Way. It's Bronte Provincial Park. Admission is charged.
This park has a combination of open grassy areas and some light forest. Once you pay admission, the parking is included.
It sometimes has indigo bunting, but I don't know if May is too early. It's not a birding location that I'm very familiar with but it's convenient to the highway.
The Rattray is nice but technically they want you to stay on trail which is limiting given there are no trails deep into the marsh. It's a collection of trails and boardwalks through a mature pine/hemlock forest; a fairly open ash forest/grassland; and a cattail marsh. It has a small creek running through and widens out into a pond area that empties into Lake Ontario along a shingle beach.There can be heavy foot traffic from the dog walking brigades although the birds don't seem to pay any attention to them. I'm not sure how much is there that isn't readily seen in NS though.
I'm not sure, but it sounded on the news like the Gardiner Expressway into Toronto is going to be under construction all spring/summer which might slow down accessing Col Sam Smith and/or Humber Bay East. Those are popular birding spots but again, not sure how much is there that is unusual. Checking eBird a few days before is probably a good idea.
eBird shows some other popular spots much closer to the airport, including Claireville Conservation Area. You might want to check the Hotspot listings for them to see if anything catches your eye.
http://ebird.org/ebird/hotspot/L1019528 etc.
Also, if you're coming in along the Gardiner, if you want to see Northern Rough Winged Swallows, they nest in the sand bluffs in a very small park called Arkendo Park in Oakville. To get there, you drive south on Winston Churchill from the QEW till it ends at the Lakeshore. Turn right, and almost immediately turn left into a side street called Arkendo. Drive to the end of the street where it makes a loop. Park. Follow the short gravel foot path almost to the Lake. Enter the dirt footpath into the "woods", and turn on the right branch for a few yards down to where you can get onto the beach. Walk along the beach admiring the swallows as they zip over the Lake and perch on the exposed tree roots in the bluffs outside the nesting holes. (Even if they aren't nesting yet, they've been reliably in that location for the past several years. They are back there already this year. There are usually also some common terns and ring billeds around but not much else is dependable. It does get a few migrant warblers in season but it's an extremely small park (the accessible part) which limits what can be found. It's good for the swallows though if they aren't ones you're used to seeing.
If there are specific birds you're looking for, be sure to ask if anyone's seen them!
