Look here for info about weather.
At the end of May, it will probably be low 20s - nice and warm but not humid. It shouldn't be too rainy - I'd bring spring clothes and a few long sleeves. Last year it was hot at the end of may - I got sunburnt & DS spent most of his time in shorts & T-shirts.
Weather.com does a 10 day forecast which may help nearer the time.
Your hotel is in a really good location - not far from the beach and right by the shops .
Things to do in the evening... If you like Jazz, you could try Andy's - you can eat there.
Blue Chicago is meant to be good for Blues music (obviously) but I've never been.
You could go to Second City Comedy club which is where lots of well known comedians started out (including John Belushi, Bill Murray, Mike Myers)
There is also the Chicago symphony and probably lots of live events around the city. You should try to see the fireworks at Navy Pier on a Saturday or Wednesday night.
Will pop back if I think of anything else.
Any questions?