Another Native here so will weigh in with my thoughts. We do "date night" a couple times a year downtown so have stayed at many of the area hotels.
While I understand that many natives would say to skip the Seattle Center/Space Needle I might respectfully disagree...in part. It IS fun to go to the top. Kids will love it. In fact, both of my boys have had birthday parties up there. One to to the top just for viewing, and another with 2 of his foodie friends, for dinner (while they could still order of the kids menu). Sure, it's touristy but the view IS cool and it is fun.
The Seattle Center (at least as it stands today) in and of itself though...yeah, not much there. It can be fun to park up there though and then ride the monorail downtown..goof around there and then ride back. The duck is fun but....a bit of a time suck in my opinion. Cute though. I think the Seattle Children's museum is a bit meh, the Everett one (not close to anything of course, is a ton better). However, the Museum of Flight is not to be missed if you have any plane buffs at all. You'd want a car but it really is a wonderful experience.
I am going to presume that most activities families are interested in (in Seattle) will include the Seattle Center, Waterfront/Pike Street Market and possibly Pioneer Square areas.
Being as many that go on Disney cruises are families, and most families are on budgets . . .
I am asking the others to suggest/share their best thoughts on family friendly hotel stay for a family with say 2-4 kids with:
1- Inexpensive or some ability to cut expenses on meals by either having free breakfasts or cooking abilities in the room.
2- that are close to Westlake Center, Seattle Center for ease of transportation as these seem to be the hub of downtown for connecting to one place or another.
3- Safe walking
Thanks in advance
For a basic hotel, the Sheraton really isn't bad. It is very centrally located, you could walk to just about anything. While I'm not (at all) a chain hotel kind of person, I have stayed there on business more than once and it's fine. The Westin is less central as is, in my opinion, the Hyatt. It's funny the difference a block or 2 can make. If you are taking the light rail in...it takes a while and the closest you will be to any hotel is at least 2 blocks. For the experience and price..it's fun, Dh and I did it once heading to Inn at the Market after a trip to Cali to avoid having to park our car. Having done it once...I'd probably take a cab or a shuttle if it were me coming into SeaTac.
In my opinion, you will get far more for your money (the same as staying at a bigger name hotel like the Sheraton) though the Kimpton line of hotels (Alexis and Monaco) or the Edgewater. If you want to really splurge, the Inn at the Market. All often have great deals online and typically
AAA specials. We were at the Alexis just before Christmas, on a killer deal for a one night anniversary getaway and got an unbelievable upgrade at check in. I have pictures of our EMP suite! Join as a "one touch" member if you plan to stay there and you will be treated well. Bear in mind I had NO status with Kimpton at the time, I'd lost my old number and re-registered. As far as they were concerned it was my first visit. From the Alexis we walked to a show that evening, and then all over town in the morning, it's a great location.
To me, the customer service you will find at these more "boutique" hotels at the same price makes all the difference in how you experience the city. Some will have breakfast packages. I can't say I've looked for family friendly downtown but do know I'd be comfortable taking my kids to any of these locations.
I'm a lifetime Seattle resident, so I'm happy to help anyone who has questions!

I'll give my advice for stuff below.
I do NOT suggest Seattle Center and the Space Needle. There is WAY better stuff to do in Seattle than go here. If you can see the needle from the ground you've seen it - it's really not a big deal. If it is sunny and you want to see the view from the top of the needle, then go - but otherwise, you'll have more fun elsewhere.
Must Do's of any Seattle visit:
You have to visit Pike Place Market, obviously!
http://www.pikeplacemarket.org/
Do the Ride the Ducks Tour to see a lot of Seattle and get some history:
http://www.ridetheducksofseattle.com/
Seattle Underground tour is an awesome way to get history of the city as well as see some really cool stuff in Pioneer Square:
http://www.undergroundtour.com/
Additional stuff:
If you want to see a spectacular view of the city and a beautiful neighborhood, head to Kerry Park:
http://www.gonorthwest.com/Washington/seattle/viewpoints/kerry.htm
If you are a huge music fan go to the EMP (Experience Music Project) at the Seattle Center. A fantastic and interactive museum:
http://www.empmuseum.org/index.asp
Hotels I recommend: (linking you to the reviews at trip advisor for them):
Inn at the Market: For the quintessential Seattle experience!
http://www.tripadvisor.com/Hotel_Re...ews-Inn_at_the_Market-Seattle_Washington.html
The Sorrento Hotel: Lovely, amazing hotel. We stayed here for our wedding
http://www.tripadvisor.com/Hotel_Re...ws-The_Sorrento_Hotel-Seattle_Washington.html
The Alexis Hotel: Another beautiful hotel close to the Market:
http://www.tripadvisor.com/Hotel_Re...Hotel_a_Kimpton_Hotel-Seattle_Washington.html
Hotel Monaco:
http://www.tripadvisor.com/Hotel_Re...attle_a_Kimpton_Hotel-Seattle_Washington.html
The Fairmont Olympic: A Seattle Classic.
http://www.tripadvisor.com/Hotel_Re...rmont_Olympic_Seattle-Seattle_Washington.html
The Arctic Club Seattle: This is an awesome hotel that was recently built from a building that was originally a gentleman's club during the Gold Rush area. It's an awesome building with historical architecture, and a beautiful hotel:
http://www.tripadvisor.com/Hotel_Re...eTree_by_Hilton_Hotel-Seattle_Washington.html
Suite type hotels such as the Embassy are not as easy to find in good locations here in Seattle. If you must have one I suggest the Homewood Suites on Pike Street:
http://www.tripadvisor.com/Hotel_Re...on_Center_Pike_Street-Seattle_Washington.html
I trust trip advisor in general for hotel recommendations:
http://www.tripadvisor.com/Hotels-g60878-Seattle_Washington-Hotels.html
Websites about Seattle:
http://www.gonorthwest.com/Washington/seattle/Seattle.htm
http://www.downtownseattle.com
Places to Eat:
Wild Ginger:
http://www.wildginger.net/
The Pink Door:
http://thepinkdoor.net/
Palisades:
http://palisaderestaurant.com/
Metropolitan Grill:
http://www.themetropolitangrill.com/
Ray's Boathouse:
http://www.rays.com/
Purple Cafe and Wine Bar:
http://www.thepurplecafe.com/
Palace Kitchen:
http://tomdouglas.com/index.php?page=palace-kitchen
Icon Grill:
http://www.icongrill.com/
Dahlia Lounge:
http://tomdouglas.com/index.php?page=dahlia-lounge
Top Pot Donuts is amazing:
http://www.toppotdoughnuts.com/
Other waterfront/downtown/belltown locations
I would add 67 to this list, Etta's Seafood for a killer brunch, Cafe Campagne, Campagne, Flying Fish and El Gaucho. There are more but I'm blanking at the moment! Ray's and Palisades are nowhere near downtown so unless you have a car, it's a pricey cab ride.
I love most of the restaurants listed above. However, depending on the ages of kids, I might not suggest them as a family location and the Met is crazy expensive. Serious Pie is great for kids. Some of my kids downtown favorites: Rock Bottom, Gordon Biersch, Elysian Fields, Hard Rock Cafe and the Old Spaghetti Factory (near the waterfront), Ivars, Anthony's (any of the 3 locations on the waterfront) and they always love PF Changs (at Westlake).
It's still a couple of hours outside Seattle, but the small town of Sequim (pronounced "Skwim") is a popular recreation destination in this area, and this is a good deal:
http://www.livingsocial.com/escapes/209480-olympic-peninsula-inn?msdc_id=1729-seatlle-citywide
LivingSocial had a few hotel deals outside of Seattle.
One is for a picturesque little town called Leavenworth, that's set up to look like an old German village:
http://www.groupon.com/deals/ga-m-a...s=body&d=ga-m-adventure-inn&p=1&c=deal_button
The other is for Friday Harbor, a big whale watching area near Seattle:
http://www.groupon.com/deals/ga-m-r...&s=body&d=ga-m-roche-harbor&p=2&c=deal_button
I haven't stayed either place, but they are both good deals, if they coincide with your cruise.
These are all quite far from the city, day or overnight trips of their own. 2+ hour drives, ferry rides, etc. Wonderful places but a closer getaway would be Salish Lodge up at Snoqualmie Falls. 45 minutes if traffic cooperates. Gorgeous getaway (think Wilderness Lodge but a bit more elegant) and amazing amazing food.
There is wonderful hiking all over, if you want to get a little bit out of town. I do recommend the aquarium, though it has been quite a while since we've been there.
For anyone who is a Seattle local, can you recommend the must have places to grab some food? DH is all about dining he is a foodie so we have a list of some places we are considering eating(all if possible)...
Poppy
Dahlia Lounge
Serious Pie
Six Seven for Brunch (I chose this because I want to eat on the waterfront)
Top pot dougnuts
Pike Brewing
many vendors in Pike place

and a few coffee shops about town
We thought of doing one of the Savor Seattle food tours but we aren't sure it is worth $70pp?
Thanks for any help!
There are a TON of great brewpubs with better beer than Pike. LOL! I love the Alibi Room, which is at the market. Not a brewpub mind you but just a fun little place. Great beer selection and fun food. 67 is great for dinner as well and if it's summer, a wonderful patio. I personally love Etta's for brunch but there are a ton of good places downtown for that.