Both Uber and Lyft apps allow you to enter both a "from" and "to" location that is nowhere near your current location.
Thus you can simple open the app, enter DTW as the pickup location, the location of your wedding as the destination, and it will give you a price for that journey.
This allows you to confirm that taking such a journey is feasible, and roughly how much it will cost - although obviously the cost can vary based on the time of day/traffic/etc.
Looking at the moment, Uber is quoting a little under $40 from DTW to Ann Arbor.
travel.stackexchange.com/users/984/Doc
Also consider the Michigan Flyer https://www.michiganflyer.com/
A bus from DTW to Ann Arbor that goes 13x a day.
travel.stackexchange.com/users/108867/DumbTownie
I'm not a local, but a while ago I worked at Ford and lived in Ann Arbor for a time,
so I did that commute every day.
Your main gotcha is going to be the state of
I-94 (and I-275 as an alternative route).
This can be very bad in rush hour.
If you're arriving in the evening after 7pm, you should usually be safe.
If you're getting a hotel for the weekend, consider that Ann Arbor is not a small area, and it has limited access to I-94 along the west side.
If you want to minimise costs from the airport, then staying somewhere in the south-east or east of the city should make your Uber cheaper.
Assuming of course that someone local can give you a ride to the wedding.
travel.stackexchange.com/users/46293/Graham
I write this answer from a Lyft going from Ann Arbor to DTW.
Booking this ride on Lyft cost $50, whereas it was $100 on Uber with surge pricing.
I’ve seen it as low as $35.
So yes, for convenience, Uber and Lyft definitely work.
But as other answers mention, there are better options for more like $13/trip.
travel.stackexchange.com/users/108874/Evan Weissburg
Since you said you want personal experience, I have made this trip a few times via Uber while visiting Ann Arbor.
It should be reasonable, though my last trip was 2 years ago ($36 at ~8 AM).
There can be a large amount of traffic slow down in the morning on a weekday, as Graham's answer indicates.
The pickup time was a bit longer than I was used to, I think it took 10-15 minutes for the driver to arrive at the Airport.
I also took an Uber from the hotel to the wedding venue, it is a very common area for weddings
so the driver should be familiar with where to take you.
travel.stackexchange.com/users/78776/ShadowTiger
Rent a car for cheap.
I was just in Ann Arbor a few months ago.
My wife goes all the time.
If we are there for only a day, Uber makes sense for a one time round trip from the airport and back.
If you are there for more than one day, rent a car.
Unless you want to burden family members with schlepping you around, it’s more convenient for everyone.
Plus, Ann Arbor is a pretty nice area.
And, except for rush hour, the drive is easy.
It would be worth the $20-30/day or so as long as you do not have to pay for hotel parking.
We usually don’t.
travel.stackexchange.com/users/108254/Dean F.
My family is going to a wedding in Ann Arbor. From a map, it looks like it's within reason to Lyft or Uber from the DTW airport. (Where "reasonable" means something like "under $50".) Does this make sense or are there any gotchas?  I know this can be calculated with the app (or various online price estimators), but I'd really love to hear from a local or someone else with personal experience.
Is Ann Arbor within reasonable Lyft/Uber range of DTW?
travel.stackexchange.com
<airport-transfer><ride-sharing><michigan><dtw>
travel.stackexchange.com/questions/154378
travel.stackexchange.com/users/4428/mattdm
Uber and Lyft are both recommended. Lyft has been reported to be cheaper than Uber. Depending on times and surge pricing,  Uber may charge between $40 and $100 for this trip. Uber and Lyft are both options, costing between $36 and $100 depending on surge pricing.
Uber and Lyft are both feasible options. Prices can range between $36 and $100 on Lyft and Uber depending on surge pricing.