Museum admission in Chicago is on the pricey side, in my opinion. The new Modern Art wing isn't worth any price you pay including free in my opinion unless you really like "art" made with trash, paint cans, etc. The old part of the museum is definitely worth a stroll through and you can photograph (without flash). Like analog photography, the original part has wonderful old master examples of analog art. The restaurant on the west side of the new wing is gourmet and the prices reflect it. Here is a picture taken from a lunch table on the outdoor dining area of the restaurant.
I found this display to be the most interesting part of the modern art exhibit. These are two engines from the Looking Glass aircraft. Google it if you are not already familiar with that chilling bit of Cold War history. In the background you can see the music shell designed by architect Frank Gehry and constructed of Titanium sheets. Grant's and Milleneum Parks are free as is the Lincoln Park zoo with plenty to photograph. Take the bus to Lincoln Park using the CTA pass (see below).
Free, is the tour of the Chicago Cultural center that is across the street and a block or so west of the Art Museum. This is the original Library and it contains a huge-maybe the largest-Tiffany domed ceiling. If you are there on Wednesday (check the days to be certain) at 12:30 there is a free concert given in the center under the dome, in the large room that was originally the reference reading room. You could do far worse by selecting and paying admission to a concert elsewhere.
Free, is museum admission at the Art Museum and I believe the Field Museum on one evening per week from 5:00 - 9:00. Check at the Cultural Center to find out details and to determine what is happening during your visit. That said I suggest you begin by taking the EL into the Loop (see below for pass information), and then begin at the Cultural Center to plan your days.
Directly across Michigan Ave. from the Art Museum is the Russian Tea House. It's great for dinner, or for high or low tea if you can afford the price of admission. If not, then continue a block or so beyond the Tea House on the same side of the street to Bergdorff's cellar where you can get good German food and lager. The cellar is open at noon for lunch but the restaurant is open for dinner. Prices are reasonable and the food is better than your average pub.
For transportation in Chicago, go to any of the currency exchange stores where you can buy a CTA (Chicago Transit Authority) pass. Get a CTA route map while you are there. The cost is around $20 for three days and the pass is good for any CTA bus, or train (called the EL for elevated). You can get on/off as much as you like and the pass begins and ends from the time you first use it. There is an on/off bus that is privately operated and costs about $25 for a one-day pass. It runs a fixed route and is marginally worth the cost. I say marginally because the wait for another bus can be long and in season the double-decker open-top busses are often full.
The two towers are the places to see the city providing the weather is clear. There is the Hancock tower and also the Sears tower (now renamed Willis for the current lesee that is I believe a UK insurance company). Admission to both is about $20 but is worth the price for photography in CLEAR WEATHER. The Willis tower is probably the best for its slightly higher viewpoint and "open air" balconies for which there is no extra charge.
Just off Michigan Ave. toward the lake (Huron St. I believe) is the Elephant & Castle pub. Good food, decent prices, and English ale on tap. We ate dinner at one of the outside tables and were astonished by the number and frequency of emergency vehicles passing by, until we realized that the next block from the pub contains a major hospital with its emergency room entrance.
Finally, the place to go for a Chicago Dog is any one of the Potrillo's chain of restaurants. You can always find good and relatively inexpensive food in Chicago. Don't forget the US custom of tipping about 20% (before tax) for service given in any restaurant that provides table service by waiters. No tipping for cafeteria-style self-serve places.