First Eagle Eye is a very good golf course and worth a look, but it is in East Lansing and this is a thread about Detroit public golf. If East Lansing is part of Detroit (Solid hour and half from Detroit w/out traffic) then we can talk about courses in Flint, Battle Creek, Marshall, etc.
Hunter's Ridge is a solid Jerry Mathews course and I enjoyed it alot (one of it not my favorite Mathews course). It is a solid hour or more out of Detroit (Howell, MI).
Brae Burn is a old golden age course by the same architects that did Indianwood Old (Wilfred Reid and John Connelan). If you are playing this course, it had best be early or late in the season as there is a landfill DIRECTLY across the street. If playing in the hottest months of summer, I have heard the smell can be quite bad.
Hilltop does have two orginal holes (circa 1919 that appear to be Reid and Connelan) that are very good and there are two or three Mathews holes that are good to OK, but after playing the orginal holes, I can not help but urn for the original 9 holes over most of the Mathews replacements and new holes.
Calderone Farms is avery good course, with some geometric Raynor-esque greens. It is IMO one of William Newcomb's best orginal designs. It was built on a rolling piece of farmland that has some very good holes and one awfull one (adjacent to Deer Museum). Good pure golf, as of two years ago they did not have a clubhouse.
Westwynd is a great public course. Terrific rolling terrain, good layout with alot of varriety. I would not see a reason to seek out Hunter's Ridge, Calderone Farms, or other courses over an hour away if you are lookin for a solid pulic course in close proximety of downtown Detroit.
Others that have not been mentioned that are solid in the Detroit metro area:
Blackheath GC (mini Lakewood Shores Gailes by Kevin Aldridge)
Rouge Park GC (old 1920's Detroit park course - sporty / old)
Glen Oaks GC (old Reid / Connelan former CC now muni)
Moose Ridge GC (solid newer Ray Hearn design).
Pontiac CC (old 1920's Ernest Way design)
Inkster Valley GC (new Harry Bower's design in Rouge River flood plane - some decent holes)
Chris