Hi Anton,
Because of the nature of your business (web design), you fall into a funny category in Google's handling of the SERPs. If you were a plumber or a doctor, the answer would be simple, but Google hasn't shown local results for queries like 'web design Edmonton' since 2010. Both website design and SEO firms all got knocked out of the true Local index at that point, and so, your efforts for rankings actually have to be viewed as organic, rather than local, because of this oddity.
What are you seeing when you simply search for 'web design' from an Edmonton-based device? Are you seeing organic rankings of any local companies, or are they random, national businesses. When I search for web design from my computer, I don't get any companies in my town (despite the fact that my own website design company is located there!) What I do get is big, monster design firms and entries from things like Wikipedia giving definitions of the term 'web design'. So, that leads me to view a search like 'web design' as a really broad search. I'm not doing a technical analysis of each of the top 10 listings, but whatever their authority is, Google is showing them to me, and it appears to have nothing to do with my locale.
Do this same search yourself, and I would bet you are seeing the same. If so, this means that ranking for the broad term 'web design' would be a matter of major organic SEO work (and probably not something most web design companies are even aiming for) simply because of the scope of the competition. Now, if you are seeing something different than what I'm describing, that would be worth noting, too. If Google is showing Edmonton-based companies for the broad search, that would be very interesting to me to know.
At the end of the day, regardless of what Google is displaying, everything must be viewed from an organic mindset rather than a true local one, because of Google's handling of web design firms.
Hope this helps!