I think that is an awesome idea. It is a very user friendly idea. Back in the day, the first mortgage company to add a mortgage interest rate calculator to their site experienced a tremendous increase in organic traffic and page rank. Tools like this are so helpful, therefore the engines like them. What is good for the seacher is good for the search engine.
To address your concerns -
• I don't believe you need to worry about a weakened link profile. There are two reasons for that, the first being these are going to be local businesses and that is never a bad thing to have. Secondly, even low quality links serve purposes. As long as these links generate traffic for your sight they are doing their job and you have nothing to worry about.
To address your positives-
• This is something I myself would use. You are right, unless you already know where the dwindling arcade is located, you can hardly find places like this.
• Getting local businesses to take part in this opportunity could significantly increase your traffic, which inevitably will increase your rankings. More impressions, more clicks, more traffic, = better rankings. The link juice passed from these other sites will help boost your authority. Sounds like you have a really great idea here. You will have to tell me when the app is ready, and if it will be available in the US 
We added a generator sizing calculator to our site in September. We have several manufacturers who link to it and sometimes direct people to go to our site to use it. We have seen a 15% increase in organic traffic since. Apps, calculators, widgits, all great SEO tools.
Good Luck!