Location

Places near Trinity Church – easy walk. There are also many downtown hotels that would fit this category.

The Baroness Hotel

http://www.baronesshotel.com/

Inn at Virginia Mason

http://www.innatvirginiamason.com/innWelcome.html

Hotel Sorrento

http://www.hotelsorrento.com

Madison Renaissance Hotel

http://www.marriott.com/hotels/travel/seasm-renaissance-seattle-hotel

Hotel Vintage

http://www.hotelvintagepark.com

airbnb
http://www.airbnb.com

Search "Seattle" for the dates you want. On the page that comes up in "Neighborhood" (to right of page, try First Hill, Capital Hill, downtown). The listing that best fit what you requested will be scattered throughout the offerings. The listing will also give you places beyond that. For example it's easily possible to walk from Belltown to Trinity in 20 minutes. NY Times says there is a service charge of 6 - 12%

Others

In this list there area few places that rent by the month.  The rates are low enough that you might do well rending for a month and only using two weeks. My guess is that they get filled up quickly during the summer.

http://www.innatqueenanne.com

http://www.marqueen.com

http://www.belltown-inn.com

http://www.mediterranean-inn.com

http://www.vermont-inn.com

http://www.pacific-inn.com

http://www.eighthavenueinn.com

Ramada Inn at 2200 5^th Ave 

     http://www.ramada.com

http://www.pikestreetsuites.com

Resources on where to stay in Seattle

http://www.cityofseattle.net/html/visitor/stayeatshop.htm

Search Orbitz or sites like it for combination airfare and hotel rates. Some deals are very good.