First I know nothing about Priceline.
If you are planning on doing site-seeing/shopping either location near Millennium Park or near Michigan Ave. would be fine. The shopping is going to be centered around Michigan Ave, with some also located near State St. The museums are closer to Millennium Park. The Art Institute is essentially part of the Park, and the Planetarium, Field Museum, & Shedd Aquarium are a short cab ride. The Museum of Science and Industry is a bit farther down the road.
As for transportation, if you are arriving by train into Union Station you will just want to catch a cab--of course this depends upon your hotel. There are a few hotels that could place you within a few blocks of the train station. In that case you can walk. Union Station is also the home of a ton of commuter trains, as long as you are arriving when it is daylight it is very safe to walk in the Loop--evenings are a bit off putting because the streets are deserted.
I am not sure when you are coming, or your budget, however this weeks edition of Travelzoo had a rate at the Sofitel Chicago Water Tower of $129.00. Sofitel is a very up market hotel. Water Tower is near all of the Michigan Ave shopping and would be a quick cab or bus ride to Millennium Park. Frankly--in this weather you will be walking VERY quickly in Millennium Park (the wind off the Lake can be brutal) and I don't know how much you will enjoy it.
You can send me a PM if you have specific questions about the city/lay out or hotels. Like I said previously I know nothing about Priceline--that question is going to be best left to another Diser.
Also keep in mind, when shopping in Chicago. Chicago and most of Cook County has a ridiculously high sales tax percentage. Often times it makes sense to buy an item and have it shipped out of state to save on sales tax or just buy it closer to your home. I know there was some talk on the boards not too long ago about the American Girl store (the poster thought she could save on shipping by purchasing at the store) however due to the high taxation rate she would have been better to pay shipping...just an FYI.