I'm going through the same process now in the Chicago suburbs, looking for a moderate house, close to the metra, in a good school district. My wife and I have decided it's a good time to buy for us and are under contract for a house in Park Ridge. While prices have come up and inventory is tight in nice areas, with a few exceptions prices in the Chicago suburbs are still below what they were at the peak. Combine that with lowish interest rates, a long term ownership horizon, comfortable monthly payments below 30% of our take home and a 20% down payment, for us it made sense to buy, especially considering our other options.
We are in the city now, and rents are at an all time high and condos/homes are selling in a matter of days. We thought about staying in the city for a closer commute to work, but talk about a bubble! Millennials and younger Gen X couples are buying up 3-bedrooms at 600 - 750K. I just don't see those increasing in value, especially once millennials start having kids and need to send them to a struggling and under funded Chicago Public School District. I know there are plenty of good schools and teacher in CPS, but it can be a struggle to navigate the system. Demographics don't support another cohort of young buyers coming in either, the generation behind the millennials is actually smaller, and I expect the city's selling and building boom to pop in the next 5 to 10 years.
I agree the Cook County property taxes are scary...but what are the options? Either pay the high property taxes in the burbs or pay high rent prices, high home prices, and possible private school tuition in the city. I didn't even mention the surge in property crime all over the city. Maybe NW Indiana is an option for some, but we really don't want to commute 2+ hours each way to our jobs in the loop. Salaries are still high in Chicago, often competitive with cities with much higher COL like NY, SF, and LA. I've kicked around the idea of going to a smaller city, but our job prospects are not as good. Definitely something to explore when we get closer to FIRE.
There's a chance prices could come down a bit as taxes and interest rates go up but that will likely be a wash on your monthly payment. Also, while there's a lot of press about Chicago's population declining, much of that has impacted low income areas while many of the "nicer" areas' population has increased. Combine that with an overall lack of open land to build more single family homes due to the cities age and natural barriers (ie-Lake Michigan), and I just don't see prices decreasing all that much for properties in the right locations over the next ten years or so.