I would check with churches. Some of them feed and shelter the homeless at night, especially during the winter.
When I was living over there, I was aware of St. Luke's Lutheran Church in Bellevue feeding and sheltering men in transition. I looked at their website, and it was arranged through the Eastside Interfaith Social Concerns Council. Website:
http://eiscc.net/ They have a list of resources that may be helpful...
EMERGENCY FEEDING PROGRAM
Bellevue First Congregational 425-454-5001 (Mon.-Fri. 9am 12pm)
Inglewood Presbyterian Bothell 425-823-9334 (Mon.-Thurs. 9:30am 12pm)
Kirkland Congregational Church 425-822-3811 (Mon.-Fri. 9am 12pm)
Newport Covenant Church 425-747-0515 (M,W 8:30am 12pm)
Saint Andrews Lutheran Church Bellevue 425-746-2529 (Mon.-Fri. 12:30 2:30pm)
Saint Margarets Episcopal Church Bellevue (T, Th 10am 2pm) 425-746-6650
FOOD BANKS
Hopelink Food Banks: (Call for days and hours of operation) Bellevue 425-943-7555
Kirkland/Northshore 425-889-7880
Redmond 425-882-0241
Sno-Valley 425-333-4163
Issaquah Food Bank 425-392-4123 (T, W Th 10am-1pm) 425-392-5836
Renewal Food Bank Bellevue 425-643-8246 (M,W 9am-12pm M 4:30pm-6:30pm)
Woodinville Storehouse 425-483-5252
Woodinville Community UMC (Tue 6:307:20pm; Sat 9:3010:20am)
HOT MEALS
Salvation Army Eastside 425-452-7300 (Mon.-Fri. 6:00pm) Issaquah Community Hall 425-679-0342 (Mon.-Fri. 5:30pm)
Holy Spirit Lutheran Church 425-883-2727 (Tues. 6:00pm)
I couldn't find anything specific to Seattle, but I bet you can find something through one of those contacts. Cheers!