Reckless Records has a shop on Madison west of Michigan Ave, walking distance from the Hilton.
For gear, try Saturday Audio on Belmont, a bit south of Wrigley Field. It’s about a block west of the Belmont stop on the Red Line El (State Street subway in the Loop). But they’re only open Thursday evenings and weekend days.
For Chicago pizza, Lou Malnati’s is good. There’s one at 805 S. State, close to the Hilton. For Italian Beef, try Portillo’s - nearest one is at Clinton and Taylor, a short cab ride. For classic Chicago, try The Berghoff on Adams or Italian Village on Monroe - the Village on the 2nd floor is the same as when Al Capone ate there.
For music, Buddy Guy’s club is just a couple blocks from the Hilton, 700 S. Wabash. Or take a cab to the 2500 block of Halsted, where Kingston Mines and B.L.U.E.S. are across the street from each other. For jazz, try the Jazz Showcase, also close to the Hilton. You’re also close to Orchestra Hall, home of the Chicago Symphony, although in the summer they play at Ravina Park in the north suburbs. There are also lots of free concerts in the summer at Millennium Park, on Michigan Ave north of the Art Institute.