Depends on if you are going north or south of downtown. Directly across from downtown is the marina. No beaches there. There are beaches south of downtown (not my area) and north (Ohio Street Beach, Oak Street Beach, and North Ave. are the big ones, but it pretty much extends north to Hollywood).
If you are going to Ohio Street Beach or to Oak Street Beach (probably the two nearest downtown), I would recommend the Fox and Obel cafe. They have great sandwiches, etc. and it would be nice place to stock up before hitting the beach. Fox and Obel is at Illinois and McClurg. If you are going to Oak Street and north to North Ave., then you have all the North Michigan Ave. and even the Old Town/Lincoln Park options.