Downtown Wausau is actually a super awesome place with tons of shops, restaurants , bars, etc. There will be likely lots of outdoor seating to eat or grab something yummy to go and eat it on the square at Red Eye Brewing Co, Patina Coffee House, Downtown Grocery, La Prima Deli, Polito's Pizza, The Mint Cafe, Malarkey's Pub. We'd highly recommend any of these places to grab a bite!
The best trail in the park if you're looking for a satisfying hike! (You'll get sweaty) Hike up to the old granite quarry and up above it for some awesome views! About 2 1/2 miles to the top. There isn't an address specific for the trail head but turn left onto Grouse Lane from County Rd NN as you're diving out of the city. The trail head is at the end! Love this hike if you're in town for a few days.
This museum is also incredibly well designed and maintained but a local artist and entrepreneur. World renowned artists and exhibitions regularly circulate through here. This does have a fee per person, but excellent curation and exhibits.
There isn't a specific address that I can find, but drive or walk north from downtown along the river and you'll come across a giant adult sized playground! Careful, metal gets hot in the sun!
Wausau's "central park" with shaded flat walking trails and giant pine trees!