Being an Edmontonian for over 23 years, I can tell you that there's not that much to see in Edmonton. But there are, however, things that you might like to see in Edmonton. YEG is damn far from Edmonton - something you'll really notice once you've landed there. I don't know if your dad's going to rent a car. If he's not, then know this - taxi fares are about $40 to downtown one-way, but the Sky Shuttle bus is about $18 return or $11 one-way - and a hell of a lot cheaper.
West Edmonton Mall is one of them. Sure, it's the biggest mall in the world, but it's got more entertainment and stuff than your average mall. It's home to the World Waterpark, one of the largest indoor waterslide parks in the world - it's still popular. There's also Galaxyland with amusement park rides and a couple of indoor rollercoasters. (the name got changed because of a lawsuit that Disney filed against the guys who designed WEM) But it's still often referred to as "Fantasyland" by the locals. The hotel still retains the Fantasyland name though. WEM even has a driving range on top of it - that explains the black netting over the roof by the waterpark. The mall is so big that it can be seen from several kilometres away because of the structure that holds the indoor rollercoaster and the hotel. WEM has recently been expanded to include an HMV music store, a Chapters and a large Playdium entertainment centre with all those video games.
Edmonton's river valley is very nice at this time of the year. It's a nice deep valley which literally contains more than half of the city's parkland. In fact, nearly all of the river valley is parkland. There are several golf courses there and lots of trails right by the North Saskatchewan River.
The downtown is not that interesting to see, but festivals take place often at Churchill Square right in front of the City Hall. The City Hall's fountainig pool is a neat spot to be when it gets hot outside. Sorry I can't quite remember which ones take place right on June 28-July 1st - I've usually been away during that time up north to see my family!
Whyte Avenue (82 Ave) is already becoming a trendy place to be - it does see a lot of people on weekends.
There's shops, bookstores (including a Chapters), bars (Don't know if you've turned 18 yet, though) and pretty good restaurants and coffee places like the Second Cup and Timothy's (once Grabbajabba, but it's still very nice - I love the chai tea there). If you're staying in downtown Edmonton and you can't take the car, take the LRT to the University station, then take the #4, 6 or 106.
I like the Chianti's Italian restaurant on Whyte Avenue. It's inside an old post office building and the food is great. Sorrentino's on Whyte provides good Italian food, too. For Asian/Japanese food, there's Grab A Bite and Tokyo Noodle House. The King And I is a great Thai restaurant - it's a challenge to find because it is right in the side of a condo building that used to be a small hospital. There's other restuarants out there, too.
Edmonton's weather is usually pretty nice at this time of the year. Usually it's around 23-26C for a daytime high, pleasant T-shirt and shorts weather.
It can get to about 28-32C, but then the humidity is usually very low. Because of the severe drought right now in Alberta, I think you won't have to worry about rain much.