Seattle is a Great City! It should not be that difficult to walk or use a cab if your hotel is downtown.
The "Fish Market" is actually part of Pike Place Market. It is a public market that has many different stands, from produce and fish/shellfish to art and crafts. It is a great place to get wonderful food and see a lot of interesting people. It is also the home of the original Starbucks.
Below the market on the waterfront are a number of seafood places. One of the more famous restaurants is Ivar's. They have excellent food and are well known for chowder. Nearby is a place called the Crab Pot. They have a special where they bring a pot of shellfish and dump it on your table. All you have to do is dig in and eat. I have never eaten there, but I often see a lot of people chowing down.
There are a huge number of restaurants around the city. You can find seafood anywhere. The better steakhouses are downtown (I like Metropolitan Grill!) If you want trendy food, then head up to Capitol Hill. If you enjoy Asian food, then head over to the International District. Finally, if you are into a very romantic (and somewhat long) evening, then try The Herbfarm! It is, in my opinion, the BEST restaurant in the Northwest. Check out the
website for more information. It is pricey, but well worth the cost.
I hope this helps! If you have any specific questions, or want more information, please feel free to PM me!