Check out Kuma's Corner, if you find yourself in the mood for a gourmet burger, I /highly/ recommend it, pinup art on the walls, rockin tunes, delicious microbrews, and all the burgers are named after metal bands! http://www.kumascorner.com/food#burgers the make your own gourmet mac n cheese bar is /fantastic/ as well.
Anne Sather is the place to go for breakfast, complimentary cinnamon rolls & good breakfast fare. Another good breakfast place is "Over Easy" on Damen, in between Argyle and Ainslie.
For Pizza, Lou Malnati's, Giordano's, and Gino's East are great, Pizzeria Uno & Pizzeria Due are...meh.
For Hot Dogs, I recommend: Hot Doug's, Superdawg, Vienna Beef on Damen.
Sushi: Sushi Para II, Shiroi Hana (which is right nextdoor to the awesome "Chicago Comics" comic book shop), Ora, Toro, and House of Sushi & Noodles (all are relatively close together)

The Museum of S & I is a fun visit (my favorite exhibit is the German U-Boat, U-505), as is the Adler Planetarium, Field Museum, and the Shedd Aquarium (check out the dolphin show there) As far as zoos go, there are 2, the Brookfield Zoo, and Lincoln Park Zoo, Brookfield is more of a tourist trap, I'd recommend checking out LPZ, the plus side is that LPZ is free admission everyday! Navy Pier is quite an entertaining place, you can also get a water taxi to the Shedd Aquarium From there.

A Cubs game is always a good time, the place is packed every home game, more than I can say for those on the South side... and the neighborhood it's located in (Lakeview/Wrigleyville) is a bustling community with lot's of things to do and see

Sears/Willis Tower skydeck & The John Hancock Building, while highly touristy are still cool things to check out.

Chinatown is pretty fun, if a bit tourist-y in some spots, also, the area surrounding Chinatown is a /dump/, Dim Sum on Sunday at Phoenix Restaurant is the /shit/.

Being a fellow musician, I recommend checking out "The Chicago Music Exchange", huge independent instrument shop, they have some really cool stuff, also being your 1st trip to the US, maybe check out the Guitar Center on Halsted (afaik large music retail shops are a uniquely US thing... I think)

Plenty of cool Bars all around the city, a few of the neighborhoods to check out for nightlife: Wicker Park/Bucktown, Lakeview, Lincoln Park,, and River North. A personal favorite place of mine is The Kingston Mines in Lincoln Park, a blues bar with live blues bands on 2 stages, looking for something smaller, there's a blues bar across the street called "Blues", among the other 30 or more watering holes in close proximity (it's like, 2 blocks away from Depaul University) other notables in the area are Delilah's (Recommend checking this one out), Aliveone, Hidden Shamrock, Trinity, Galway Bay, Lion's Head Pub. and Victory Liquors among many others.