There's nearly 6 hours to travel to the nearest border crossing at Carway, AB...
Alternatively, you could have a vacation and land at the end of it. The cheapest vacation from Edmonton appears to be for Vegas for around 500 CAD/ 3 days...
A quick search on this forum would have shown a few threads on this for example http://www.canadavisa.com/canada-immigration-discussion-board/edmonton-nearest-us-border-t306590.0.html Seems also some mention of a CBSA office in Edmonton but no details. So Carway or Coutts.
If the border is too far, you can do landing at nearest CBSA office as well. But I have heard that it takes 4-6 weeks to get an appointment. All the best.