Could anyone tell me if their is a shuttle from the airport in Seattle to downtown and if any of the hotels offer this and what is the price? Also, is the monorail accessible in most parts of downtown and surrounding areas?

Yes, the airport shuttle service is called Greyline, there is a website. It is $10.25 (i think) and does a circle of the main downtown hotels.

The monorail is only a straight line so (while fun) not particularly handy for getting around, except to go to the Seattle Center.

But Metro busses within the downtown core have a "free ride zone" which is great. Just hop on and off busses traveling along the various cross streets (1st, 2nd, 3rd, etc.). Driver will announce before the free ride zone ends.

www.graylineofseattle.com and look at "Downtown Airporter"

There is also a service called Shuttle Express that operates out of the same ground transportation area that the cabs use.

The only reason to use the Shuttle Express would be if the Grayline does not go to your destination. The Grayline is less expensive and far more comfortable.

Of if you are 2+ people you might want to spring for a taxi cab. SeaTac to downtown is ~$30.

IMHO Shuttle Express is a reasonable alternative only if (1) you are traveling alone, and (2) you are going to an outlying suburb.