Hi there. I commented before, and all of that still stands. It's such an exciting opportunity--congratulations. I disagree with many above about uprooting teens. Teens are resilient and giving them an international experience can be wonderful, especially if there's nothing to lose back home. I have a 14-year-old and I would love to relocate to the UK from Michigan just to give mine that experience. Alas, finding such an opportunity is the barrier. If you already have one, I say go for it!
Troy is a wonderful place to live for families. I would honestly stop my search right there. You're not going to find a Manchester or Birmingham in Michigan if that's what you're looking for. Although Detroit is a great city, it doesn't have appropriate facilities for children and teens. It's not safely walkable from one neighborhood to the next and I would be suspicious of the bus system (they don't yet have a rail system). It is a fun city to go to sporting events, musicals, symphonies, etc. There IS actually a Birmingham, Michigan, which is walkable and very safe, but it is very posh/expensive and probably what you'd consider a "small city" (although I suspect most of our cities would fall under that category). Royal Oak is another option for you to consider. It has a downtown area that is thriving, schools that are middle to adequate, and affordable housing. Tell me, what do you mean by "small city"?
If you live in Troy, depending on where you live, your wife will be able to walk to certain things. We lived near the Troy Historical Museum in Troy and I could walk to the grocery store, the library, the school, the community center (gym, pool, etc.) If your wife bikes, she could easily bike from that area to a large indoor mall (Somerset) or many other shops surrounding. There are many great dining options around. Troy School District is one of the best in the state, and this is something you should be VERY concerned about. The US has quite a bit of disparity between school districts. I can't stress enough to be very careful in this choice. It is unequal, and sad, but it is reality. If you want to carefully consider what district you will end up in, visit https://www.greatschools.org/. Type in a city or a district or a school name and you will find a "rating" of that school. You can also visit https://www.niche.com/k12/search/best-public-high-schools/s/michigan/ for a list of all high schools in Michigan ranked. As you can see, Troy High School is ranked #2. This means something. If you want your 14 year old to go to a particular school, you'll need to be careful to choose a house within that school's boundaries. Here is where you'll find Troy School District's boundaries: https://www.troy.k12.mi.us/departments/enrollment/district-maps
In Troy, you will certainly get the full American suburban experience. You might look at it as cultural immersion. If you are looking for one of those wonderful cities you have over there with a city centre, great public trans, green space and a lovely feel, you will not find that in Michigan. Ann Arbor is the closest you might come, and that is VERY far to drive during busy hours to Troy. I wouldn't recommend that commute.
If you would like assistance with all this, I am happy to help. I have three kids spread across high school, middle school and elementary school, so I am well-versed in this system.
Best of luck to you all!