Doe Bay on Orcas Island is the only hostel type accomodations I know of on Orcas.
http://www.doebay.com/ They normally have a two night minimum but usually if they have room and you call them at the last minute or they know they will be empty they will let you rent for one night.
Problem is you pretty much need a car to get to Doe Bay unless you bring a bike and like to ride a lot (most likely in the rain - November is the wettest month) and bringing a car on the ferry is expensive. Not sure what it will cost in the off season tho currently the fare per car w/ driver is $38.85 with an additional $11.85 for each passenger. It will be a bit less I expect since it's off season. Camping wouldn't be much fun in November - again because of the rain.
Another possibility - also on Orcas - is the Garden Cabin at Blackberry Beach in Olga. This might be cheaper than the hostel for two but I don't know if Carol Jo wants to rent for only one night. Wouldn't hurt to ask her.
http://www.blackberrybeach.com/ (We've stayed there and it's quite nice for the price. Has a small kitchen so you could save on meals.) A bit closer than Doe Bay but still probably requires a car.
The Spring Bay Inn (that Wesley gave you - also on Orcas) is way over your budget but their kayak tours probably aren't. Again you will need a car. I don't think they give all day tours since they also have to run the inn.
You did say San Juan Island which is a bit easier to get around on without a car. Unlike Orcas the ferry leaves you off at the biggest town so you can leave the car in Anacortes. I was able to find a hostel there:
http://www.hostelz.com/hostel/26974-Wayfarer's-Rest which I see is also one of the links that Wesley gave you. I was a little concerned that it being off season they might not have kayak tours but I see the Discovery has them all year round.
http://www.discoveryseakayak.com/daytours.html I would talk to your kayak people and make sure that they know you do not have a car so they don't expect you to show up on the other side of the island from Friday Harbor. Also you might be better off with a half day. I wouldn't bet on a pretty sunny warm day in November and being cold and wet and tired on your drive home is pretty dangerous. Also check when sunrise and sunset are.