I highly recommend Townshend's Alberta Street Teahouse.
It's a great spot to sit, read, listen to music or play games while drinking tea. They have a huge selection of teas (over 100!), and awesome bubble tea.
The employees there are really friendly and knowledgeable and are great with recommending teas if you can't decide on one.
Tip: On Last Thursday they usually have something going on inside - an art show or live music - which is fun to stop in for.
Keywords: Just you alone / As a single, Dress casual, With teens, Outdoor / Patio seating, Cafe / Tea House / Coffee Shop, Brunch, Internet (Free), Good for first date, Everyone, No smoking, With a group, With kids, Dinner, "In" place / People watching, With business partners, As a senior citizen, As a couple, Lunch, Breakfast, Very cheap (under US$ 5), Eating late