We would like to visit Europe for about 10 days this fall. Any suggestions as to what would be a good country/city this time of year would be greatly appreciated!
No, it will be significantly warmer in most areas north of the Alps than Chicago! I spent four winters in South Bend, and many fall trips to NW Europe. The two are not comparable.
Excluding the far north of Scandinavia and Russia, the only real weather concern at this time of year in most of Europe is that those areas with a cooler, moist climate can see some significant fog. This makes sight-seeing a little more hit-and-miss in rural areas compared to the summer.
I love Italy in November. Prices drop on Nov. 1 and the weather is great. You can't compare the weather to the same latitude in the US. It's much warmer and I'll leave it to the weather geeks to explain why!
We've been to the UK and Austria in late Nov/early Dec. It was great! Temps in the southern UK (London and environs) were usually around 40s for the highs with lows in the 30s - occassionally some cooler days. It snowed just enough to cover the groud and be pretty 2 times in 20 years. Scotland was a bit colder- highs in the 30s mostly- we got more significant snow one year in Inverness/Aviemore. Austira was lovely. One year we had light snow in Salzburg (less than an inch). Temps were usually in the 20s to 30s with some lows in the low 20s. Just wear layers, take good rain gear and plan to enjoy. We loved the Christmas markets (they open around Advent which is usually in late Nov.).
Southern destinations (Italy, Spain, Portugal, Greece, Turkey) will be really comfortable that time of year. I'd rather be there in October/November than during the summer.
Anywhere you want--I don't think fall weather restricts any particular destination, except for perhaps the Alps (depending in how late in October you get there).