Enjoy!
If you're both planning on having a few drinks, highly consider taking the Go Train into Union Station - which is right next to the arena.
I highly recommend getting there nice and early to take it all in - right outside the Union Entrance you can take some pictures at Legends Row, and then pop in for something to eat at Real Sports Bar. All right next to each other, and that will allow you to get into the Arena right next the ticket office - you can have them print off a ticket stub for your digital ticket, as a nice little momento/keepsake of your first Leafs game.
Make sure you get in before warmups as well - it's always cool to get to your seat before warmups and the crowds wash in. If you have upper bowl tickets, getting in early will let you go lower bowl and take some pics right by the glass as well - just explain to the ushers what you're planning to do, and they'll have no issues.
If you're absolutely set on driving in, then parking underneath Real Sports (15 York Street) is your best bet. It will be a little pricy, but it's right nextdoor and super convenient. There may be a little rush to get out when the game is over, but it's still my preferred location for parking.
Have fun man. Hopefully they pull out a W for you.