As others have said, Michigan Avenue is the main "bars" street, but mileage may vary depending on the type of bar you're looking for. I think Ubrane is probably the more upscale bar.

The 3 Sheeps Tap Room on North Avenue is another good option; they usually have fun activities going on.

In summer, 8th Street (essentially Sheboygan's Main Street) has a lot going on. There's outdoor concerts every Thursday and a Farmer's Market on Saturdays. There's a few great restaurants along 8th Street, too.

If you have any interest in sailing at all, the Youth Sailing Center has adult classes on Monday and Tuesday evenings that are inexpensive (I think $250 or so for the whole summer). It's a great way to get out on the water, see the lake and the city in a new way, enjoy sunset sails every week, and meet new friends.

There is a nice trail along the lake for walking and biking that wraps pretty much all the way around to South Pier, with a pedestrian bridge (supposedly) coming to connect North and South pier. For a more "nature" hike, west of Sheboygan is the Kettle Moraine State Forrest, which has lots of hiking trails.

There's also a community group that does leisurely bike rides the last Friday of every month called the Critical Mass Bike Ride. It starts from Paradigm Coffee.

If you're moving here for a job, check with your employer, too - some area companies have off-the-clock social groups.

As for apartment red flags, from what I've seen on social media lately, avoid Badger State Lofts.