I'd definetely opt for the Palmer House if you're going to be a tourist. You're only at the hotel to sleep anyway, right?

Palmer House is on state street, all the big shopping is there, "L" is within 1 blocks walk of the Palmer House as is the subway. If you want to goto museums, you can hop on the #146 bus I think it is right there (www.transitchicago.com for CTA maps) which goes to every museum but Science & Industry (awesome day trip btw), which the #10 takes you to right on state street. You can also take the red line subway on state street south to Roosevelt and walk east about 10 minutes onto the main museum campus.