Chicago trip

are there any places that are considered unsafe

tldr: The "places to go" you mentioned are okay and you don't need to worry about them, and it's likely you don't have enough time to visit other tourist attractions. Expect large crowds due to holiday and exercise your caution accordingly and plan your trip early.

I heard about the south side of Chicago but is it true that it's dangerous there or it's more of a myth? (If it's true then which area in particular should I avoid?)

Best to avoid them entirely, except for Hyde Park neighborhood where UChicago and Museum of Science and Industry are at and they are actually pretty cool. There is nothing much I find to see elsewhere in South Side either. Common advice is that don't go further south than 35th Street but it's not perfectly accurate, e.g. I would rather not walk through State Street near Dearborn Homes (26th to 30th St., just north to IIT). On the other hand Pullman on the South Side is much safer than other neighborhoods but it's not convenient to get there by 'L'. Other safer neighborhoods in the South include Bridgeport and Garfield Ridge but I am not sure what you can find in there, maybe you can help me discover :)

And try to avoid the West Side as well, although I can't define a "safe boundary" I tend to not get off the Blue Line (Forest Park Branch) at stations between Illinois Medical District and Austin and there is no point going there either.

Downtown areas and north tend to have nothing to worry about compared to the south in terms of violent crimes, but always exercise caution and watch your belongings.

The CTA 'L' is mostly fine as long as you don't ride the Red Line south past Garfield (there is no point going further south anyways) or get off at stations in unsafe neighborhoods (i.e. riding past them is generally fine) and if you use the south branch of Green Line better not ride towards the west, as the line branches off after Garfield. Getting off with crowd at 63rd/Cottage Grove during the day is okay but there is no point getting off at King Drive.

Since you are skipping museums there is nothing much I can think of right now. Maybe some shopping and eating at Magnificent Mile and Bucktown/Wicker Park, and perhaps the Big Bus Tours for sightseeing (never personally ridden it). If you are going to watch the fireworks at Navy Pier be advised the gates close early today and there will be lots of people.

Eat a Chicago-style hot dog!