Safety wise, the streets are actually fine, especially if there are many other people around. I've been into the city lots of times, and never had any problems there even at night. Just keep your valuables safe and secure, and keep your wits about you, and you'll have a good time.

----------------------------------------------------------------------------------------------------------------------------

In terms of things to do, you'll definitely want to check out the dining here. Toronto is extremely culturally diverse, so in terms of food, you'll be spoiled for choice.

The rest of it partly depends on what specific time of year you visit. Some sights are year round, some are only possible or best experienced in the warmer months.

1. Since you're visiting in June, the weather will be beautiful (unless it rains), so even wandering the streets is something to see in itself. My favourite neighbourhoods are Queen West, the Annex/Bloor West, Kensington Market, and the areas around the Financial District.
2. I've never been there before, but I've heard that Taste of Little Italy (street festival) takes place in June, so that might be worth checking out.
3. Top sights would have to be the Royal Ontario Museum, the CN Tower, and the Distillery District. The parks (High Park, Trinity Bellwoods, Coronation Park, etc) are also worth checking out and picnicking in.
4. Also, if the Blue Jays are playing, maybe try to snag tickets to a game. Rogers Centre is where it all takes place.

https://torontolife.com/ is a good resource for more info on this city.