You can usually tell a Jeep wheel bearing is going bad by a humming or growling noise from a wheel that gets louder as you speed up. You may also feel a vibration through the steering wheel or floor, and the wheel might feel loose when you wiggle it.
The sound is the biggest clue. It often starts as a low hum, almost like driving on a rough road even when the pavement is smooth, and it grows into more of a growl or grinding as the bearing wears further. Pay attention to whether the noise changes when you turn. A bad bearing on the driver's side often gets quieter when you turn right and louder when you turn left, and the opposite happens for a bearing on the passenger's side, because turning shifts the weight and pressure onto or off of the worn part.
You might also notice your Jeep pulling slightly to one side, or the steering wheel shaking at highway speeds. If you jack up the front end and grab the tire at the top and bottom, any back-and-forth play means the bearing has worn beyond a safe point. None of these signs are things to guess about on your own driveway, though, since a loose bearing can be hard to distinguish from other suspension issues without the wheel off the ground and a trained eye checking it.
Ann Arbor's mix of winter road salt, potholes, and stretches of rough highway on I-94 and M-14 tends to wear bearings a bit faster than on smooth, mild-climate roads. If your Jeep has racked up a lot of miles on local streets with frequent freeze-thaw cycles, that's worth keeping in mind when you notice any new noise, since it may be wearing parts sooner than the mileage alone would suggest.
If you're hearing this kind of noise while driving around Ann Arbor, it's worth having someone take a proper look before it gets worse. Hoover Street Auto Repair works on Jeeps regularly and can listen to the noise, check the wheel for play, and tell you exactly what's going on so you're not left wondering.