Good post Eddie, but booking less than 10 days ahead, right around July 4th, I'm skeptical of one's ability to secure anything quality much under $200. Could happen though, doesn't hurt to look.
There are some DT hotels under $150, but the consumer reviews tend to be poor.
And, everyone's "walking distance" is different. If your willing to be 2 or more miles away one way, you'll be able to cut down the rate while maintaining the quality. Heck, if you willing to be 7-10 miles away, you can go under $100 I'm sure.
Actually the Alexis is a decent walk to the ballpark and close to Pike's Market etc. At this time of year they will be around $250-$275 and they include a $20 voucher against eats at their own restaurant.
"Boutique" style but always had good experiences there.
The Edgewater appears to be booked up on that date. Here's a list of hotels with their distances from Safeco Field: