Hi Armands,
This might be a bit shocking, but I've never been a big fan of any free keyword research tool I've tried for Local SEO purposes, but then, keyword research hasn't been a daily task for me in a couple of years. It's really important for me to mention that it has been at least a couple of years since I've looked at whatever paid tools may be new, so I can't say whether their accuracy has improved, specifically for correctly representing local search volumes. When I was doing more of this, I simply used the old strategy that I remember first being recommended by Matt McGee of performing non-local keyword research and adding geomodifiers back into your list of findings, knowing that people search for most things that exist in most cities, regardless of what tools say. This may not sound sophisticated - and it isn't - but it has always made good horse sense to me. Do note, however, that Rand did an important Whiteboard Friday on this topic of how we can't do keyword research like it's 2010: https://moz.com/blog/cant-do-keyword-research-like-its-2010-whiteboard-friday
Where this gets a bit more complex is when you have geographic vocabulary differences (soda vs. pop, lawyer vs. attorney, stick horse vs. hobby horse), in which case, knowing the way your audience speaks is either going to be something you research in person, or something you approximate via Internet research of social media to see how people talk locally about the products you sell.
Now, that being said, there is one trick I'm totally fond of - the wildcard search Mary Bowling spoke of at a recent conference. I had never seen that before, and it's awesome:
http://www.localvisibilitysystem.com/2015/02/18/how-to-use-wildcard-searches-for-local-keyword-research-lightning-round-with-mary-bowling/
And, remember to pay attention to the 'related searches' section at the bottom of most Google results. There are some really obvious clues there.
And, finally, I've always thought that Google's categories provided some of the most important keywords one should be optimizing for, when you are aiming to rank well in Google's local product.
So, while I want to be sure to note that I am not a local keyword research expert in any way, I think much of keyword research is actually just common sense, but with the understanding that some of it isn't common sense and findings can totally surprise us about the way people search.
Further Reading:
http://www.localsearchforum.com/local-seo-tools-software/38694-free-keyword-rank-software-competitive-analysis-pre-consultations.html
https://www.brightlocal.com/2014/07/22/effective-local-keyword-research/
http://www.localsearchforum.com/local-content/38255-keyword-research-blog-posts-local-content.html (see CodyBaird's comment)