I would save the Chase points for more expensive cities like Tokyo or Zurich, unless you REALLY want this particular Park Hyatt. The Park Hyatt is close to aspirational, according to reviews here (I've never stayed). Nevertheless, Chicago has plenty of good hotels in the Loop and Mag Mile. For example, you could consider the Hyatt Regency Chicago or Radisson Blu. There's a difference, but they are more than adequate. It's up to you if they're "upscale".

Rates in Chicago vary widely, based on conventions, weekday/weekend, time of year, and other factors. Sometimes even mediocre hotels cost $250 per night. On the other hand, many weekends the upscale Mag Mile hotels are under $150. Next weekend, I'll stay downtown for under $125.

For redemptions, it's extremely difficult to talk about Chase points at 1 cent each, less than a Thank You point. If you must, just trade in enough for the Stay Certificates (HR Chicago takes Choice certificates, $145 per night) or a cash rate.