I assume you are asking about lodging? Based on many of the sugestions here take a look at where the Fairmont Hotel is (and there are plenty more in that area). This is a good location that would allow you to get to the Adler and Millennium Park and the lakefront. The loop is fairly dead after business hours so I wouldn't do that. An evening walk north on Michigan Avenue is really nice. If you have time during the day you can continue north along the lakefront (see: Oak Street beach) towards North Avenue beach. The views back south are great. Going to Adler to the south and North Ave beach to the north is fairly agressive. I think we are assuming that "wandering" means likes to walk distances.

Others can chime in, but I'm thinking a round trip starting at Millennium, going to Buckingham Fountain, south and east to Adler and return would take at least a couple of hours walking at a decent pace but allowing time to take in the sights. A round trip from the Fairmont to the end of Navy Pier an hour and a half (again briefly taking in the sights, but no alotment for relaxing)?