Here's the top 50: http://www.urbanspoon.com/n/1/4/Seattle/Belltown-restaurants
What I can tell you is that I arrived in Belltown with a reservation at the hostel and drove around nearly 2 hours trying to get a parking spot within 5 blocks. There is a nightclub in the area which makes free parking hard to come by on a Friday evening.

There are many restaurants within a short walk of the Hotel Max, including most of Tom Douglas' popular places: http://tomdouglas.com

What types of food and price range are you hoping for?

HTTY

Red Fin right in Hotel Max is great for breakfast or lunch. For dinner, I would head into real Belltown, but what kind of food do you like?

Contrary to what some people seem to think, Seattle is a reasonably big city. You cannot expect to park in front of your destination.

The Hotel Max is downtown, not Belltown. And it's Belltown, one word.

You cannot expect to park in front of your destination.

The OP did not state an expectation to park in front of the hotel.

The Hotel Max is downtown, not Belltown. And it's Belltown, one word.

For purposes of answering the question about restaurants, it is irrelevant that Hotel Max is located one block outside Belltown or that Belltown is one word rather than two.

We want people to feel comfortable asking questions here. Nitpicking admonishments and straw man attacks thwart that effort.

HTTY

Made a mistake. Staying at the Maxwell Hotel. As for the kind of food that we like, well I would like Italian or Seafood. Hopefully we can eat fairly close to the hotel.

Assaggio, Barolo, and Il Fornaio are three good Italian restaurants within a short walk of your hotel.

Most good Seattle restaurants offer fish on their menus. Blueacre Seafood is the seafood restaurant nearest your hotel.

HTTY

For italian I highly recommend Assagio's on 4th Avenue. Right that same area you'll also find Lola's, Dahlia Lounge and Serious Pie, three popular Tom Douglas restaurants. Il Bistro in the Pike Place Market is another great italian place. For seafood I like to go to the waterfront, to any of many restaurants with a view, like Anthony's, Elliot's, Ivar's, etc. Or Etta's Seafood or Matt's in the Market two others for seafood.

If you want to have a drink on your way to dinner, Oliver's, the bar at the Mayflower Park hotel is a really nice place you'd be walking right by to get to any of those I mentioned above.

OK, Maxwell Hotel is on the north side of Seattle Center. The suggestions here were directed to Hotel Max, which is downtown at 7th and Stewart.

Good eyes enzian! Hotel Max is downtown & Hotel MaxWELL is on Queen Anne. Nowhere near each other really. The restaurant recommendations all still hold as great palces, just they are not a "short walk from the hotel".

There are many restaurants within two or three blocks of the Maxwell. Those of particular interest include Toulouse Petit (really good Cajun) and Ten Mercer, where I always order the Penn Cove mussels with yams, seed bread, and spicy curry sauce (really delicious). Among the ethnic restaurants, Racha Thai is a standby.

HTTY

For seafood in Seattle, hit up Seastar Restaurant - it's not that far - www.seastarrestaurant.com - 2121 Terry Ave, Suite 108. Get a 'little' out of your hotel deal - cruise over to Portage Bay Cafe on Terry Ave in South Lake Union for awesome lunch, brunch & breakfast - 100% organic, locally sourced - www.portagebaycafe.com

In Belltown - Umi Sushi is an awesome restaurant and always packed, a good sign. They have great sushi and a very popular happy hour - www.umisakehouse.com

And happytrails guy - Hotel Max really is in downtown - the 'real' part of Belltown is much further away than 1 block, for all intents and purposes as you say. And anyone saying they drove around for 2 hours to find parking - really? No, not really - that's a gross exaggeration.

<drove around nearly 2 hours>

You have to be willing to pay to park in a garage or lot downtown these days. Or at least stuff quarters in a meter (and that's only a 2 hour limit).

There were not even any spots in the pay lots or the parking meters.
I finally caught a break on a free spot only 1.5 blocks from the hostel I will never go to again.
By the time I got signed in, I was stuck on an upper bunk in a room with 5 other guys.

<There is a nightclub in the area which makes free parking hard to come by on a Friday evening.>

Of course you are not going to get free parking in downtown Seattle on a weekend evening, that's not a realistic expectation. But I'm having a real hard time believing that every single space in every single parking garage and parking lot was completely full. That seems kind of impossible.

And happytrails guy - Hotel Max really is in downtown - the 'real' part of Belltown is much further away than 1 block.

Thanks for the news. I didn't know that some parts of Belltown are unreal: “The neighborhood [Belltown] is bounded on the north by Denny Way, beyond which lies Seattle Center, Uptown, and Queen Anne Hill, on the southwest by Elliott Bay, on the southeast by Virginia Street, beyond which lies the Pike Place Market and the rest of Downtown, and on the northeast by 5th Avenue, beyond which lies the Denny Triangle.”

Our favorite parking deal in Seattle on weekends and after 5:00 p.m. is in the building where Palomino Hotel is located. Palomino has a great happy hour, and they validate parking.

HTTY