I stayed here in early January during the intro weekend special of $119/night (note, best weekend rates are currently $159-169).
It's your basic Westin. Heavenly Bed (with the 50/50 sheets). Modern urban styling like all new Westins seem to be.
I was upgraded from a standard room to a lake view room. Problem is that since most rooms face south or north, you have to stand by the window and look to the west to see the lake. Not worth the extra $.
Location is good in that you have access to many restaurants at Lincoln Square and Bellevue Square without going outside. But same could be said of the Hyatt except you woud have to brave the elements for a block.
I self-parked at the underground parking at Lincoln Square. I asked at check-in about how to handle parking if you self park. They weren't very informed or helpful. Based on my results, you can self park there overnight with no charge (parking at LS is free). So unless you really benefit from valet parking (or you're on expense account), save the expense. There is an elevator on the south end of the garage that takes you to the Westin lobby.
There were a few simple design things that bugged me about the Westin. First, they had premium beers in the honor bar that were not twist-off, but there was no bottle opener in the room. Second, it required two key uses to access the fitness/pool area. And the key access to the fitness area is oddly placed (read some distance) from the door.
I haven't stayed at the Hyatt so I will leave others to compare. But, for the money, I'd prefer to stay at the Sheraton. They have Sweet Sleepers which are comparable to the HB, IMO. They also have Starbucks in the room. And they have a Club Lounge (or when closed, they offer one free breakfast entree and beverage). Parking is also free (albeit outside). The one downside to the Sheraton is poorer location.