A good place to start is to go to some websites about edmonton so you can do what you like
http://www.edmonton.com/for-visitors/coupons.aspx
the coupons change month to month though some stay on for months.
http://www.edmonton.com/for-visitors.aspx
http://www.edmonton.ca/
http://www.discoveredmonton.com/
http://www.infoedmonton.com/
http://www.destinationedmonton.ca/
Play in th foutains at Alberta Legislature Building or in front of city hall.
go for a river boat ride on a paddle boat down the river valley or go for a walk there some great trails for walking or rollerblading or biking.
Museums
Art Gallery of Alberta to admire more than 6,000 priceless artworks if you are going to be here the last thursday of the month it is free from 6 to 9 pm.
Royal Alberta Museum with its astounding display of fur trade artifacts and Canada's most extensive collection of mounted birds. http://www.royalalbertamuseum.ca/
The country's largest living history museum—Fort Edmonton Park—fascinates history buffs as they stroll through the streets of four historic periods spanning 1846 to 1920
The Muttart Conservatory, an expansive horticultural spectacle, is noted for its unique perimades shape.
Telus world of Science http://www.edmontonscience.com/pages/home/default.aspx
John Walter Museum
http://www.edmonton.ca/attractions_recreation/attractions/museums_historical/john-walter-museum.aspx
Also there is downtown's eclectic neighbourhoods, such as Chinatown, the Avenue of Nations and Old Strathcona District, delight visitors from all walks of life.
since i dont know when you are coming here are some of the events coming up
Aug 4, 2010 Aug 8, 2010 Edmonton Folk Music Festival The global stars of blues, Celtic, bluegrass, gospel & world music come together for five days where… Gallagher Park
Aug 6, 2010 Aug 8, 2010 Animethon17 "Anime" aims to provide a place for the appreciation, exploration, & education of all the facets of… Grant MacEwan University
10700 104 Avenue,
Edmonton, AB
Canada T5J 4S2
Aug 6, 2010 Aug 8, 2010 Cariwest - Edmonton Caribbean Arts Festival Cariwest brings the spirit of Caribbean Carnival to the Festival City of Edmonton. Various Downtown Locations
Aug 12, 2010 Aug 22, 2010 Edmonton International Fringe Theatre Festival The world's second largest Fringe Theatre festival. Old Strathcona area
Aug 13, 2010 Aug 15, 2010 Stony Plain Cowboy Poetry And Country Music Festival 2010 To edify, educate, and elucidate the traditional cowboy life and humor in music and prose...mostly r… Stony Plain-Exhibition Park
Aug 14, 2010 Aug 15, 2010 The Edmonton Latin Festival The Latin Festival’s goal is to bring awareness to the uniqueness of Hispanic heritage, creating opp… Sir Winston Churchill square
Aug 20, 2010 Aug 22, 2010 Edmonton Dragon Boat Festival EDBFA promotes Dragon Boat racing & multicultural celebration for fun, sport & recreation to showcas… Louise McKinney Park
Aug 20, 2010 Aug 22, 2010 Edmonton’s Labatt Blues Festival Blues International presents the 12th Annual Edmonton's Labatt Blues Festival Hawrelak Park Amphitheatre
9330 Groat Road
Aug 21, 2010 Aug 21, 2010 Canadian Derby 2010 The Canadian Derby is a Canadian Thoroughbred horse race run annually at Northlands Park. Northlands Park
Aug 12, 2010 Aug 22, 2010 Edmonton International Fringe Theatre Festival The world's second largest Fringe Theatre festival. Old Strathcona area
Aug 20, 2010 Aug 22, 2010 Edmonton Dragon Boat Festival EDBFA promotes Dragon Boat racing & multicultural celebration for fun, sport & recreation to showcas… Louise McKinney Park
Aug 20, 2010 Aug 22, 2010 Edmonton’s Labatt Blues Festival Blues International presents the 12th Annual Edmonton's Labatt Blues Festival Hawrelak Park Amphitheatre
9330 Groat Road