Lakefront: Few visitors realize that downtown Chicago has a park, one of its best attractions, that runs 18 miles along the lakefront. There is a paved path running the entire length that is great for biking, running or walking. Bikes can be rented at several places, including Navy Pier, Millennium Park and North Pier. It can be crowded in the summer, especially near Navy Pier and North Avenue Beach, but as you get away from downtown it opens up and offers spectacular views of the city and lake. You can ride north to Lincoln Park Zoo or south to get a great look at the city over the water. There are several sand beaches, the best of which are Oak Street Beach and North Avenue Beach. Both beaches are very busy in the summer and contain restaurants, concession stands, restaurants, and volleyball courts. Parking is very limited and taking a cab, bus or walking is the best option.
Views: Having a beautiful skyline and lake provides downtown with many spectacular views. The Sears Tower and Hancock Building both offer amazing views from almost 100 floors above the ground. Both charge over $12, although the Go card or Chicago City Pass offer admission, and wait times can be up to an hour. An alternative is to go to the Signature Room Lounge on the 96th floor of the Hancock Building. It has no cover charge and the wait time to get on the elevator is usually less than 10 minutes, except on the weekend. It also offers a pleasant atmosphere and a place to sit and enjoy the views. It is one of the best places to go downtown. The Michigan Avenue bridge affords great views of the waterside buildings and of the Mag Mile which is especially nice around Christmas. Navy Pier has great views of the skyline from over the lake, especially from the ferris wheel. Walk five minutes to a small park just northwest of the Navy Pier entrance for a pleasant panorama of the entire north lakefront skyline from platforms that juts out over the lake.
Transportation: Chicago has a good, safe public transportation system. There are buses that run to all of the main sights and attractions. They will take you to almost all of the places you may want to go. The CTA, Chicago Transit Authority has a good website, transitchicago, for planning your route. The trains are called the "EL", short for elevated, and yes it is still called the EL even when it is a subway. The trains are the best way to get to both of the baseball stadiums. I do not take the train to the United Center and do not take the train south of U.S. Cellular Field. Both airports have trains that run to downtown and they dead end at the airport so you can not go the wrong direction. It offer a $2.25 alternative to a $30-$40 cab ride and because of traffic it is sometimes faster. Michigan Avenue has several buses that will take you to all of the major museums, Millennium Park and to Lincoln Park Zoo. The drawback to the CTA are that trains and busses can be late, can be very crowded and you must have exact change.
Free stuff: The obvious free thing to do is walk around the city and take in the beautiful buildings and people watch. Chicago has a surprising number of outdoor works of art by world famous artists, such as, Picasso, Miro, Chagall. It has many outstanding parks, like Grant Park, with Buckingham Fountain as it's center piece. Lincoln Park with it's free zoo and conservatory offers free entertainment for the whole family. Millennium Park has a lot to offer as does the lakefront. When the weather is warm the pavilion at Millennium Park has free jazz, classical or just about any type of music concerts. The Symphony often practices at noon. Many of the museums have a free day, usually on Tuesdays.
Safety: Most of downtown is quite safe, especially anywhere near the tourist attractions. Do use common sense however. West of downtown and parts of the area south of downtown can be dangerous. Millennium Park is secure. Trains and buses are very safe. Homeless people may ask you for money, but they will not hassle you and are generally polite. Do be careful if they say they just want to ask you a question. They almost always end up asking for a handout but they are safe. I usually just say sorry I am busy and walk away. Be careful crossing the street. I see countless visitors walk in front of cars walking against the light. Especially when oncoming traffic has a left turn arrow.