Do you have passports? If so, you must add Vancouver to your list of places to visit. Also with passports you could take a ferry to Victoria on Vancouver Island. Do you like hiking? Mt. Ranier would be a fun spot.
Mount Rainier National Park - Mount Rainier National Park - I believe a $15 parking pass gets you 7 days entrance to the park. There is an underground tour in Seattle I have always wanted to take that is highly recommended
UNDERGROUND TOUR. This is different than the
underworld tour offered by the same company. Also really fun is ocean kayaking in the Pudget Sound. You can go on a guided ocean tour. My teens would really enjoy this, so maybe yours would too? I did an overnight trip once and I cannot remember who we used, but I think it was these guys
Kayaking San Juan Islands: Whale Watching Kayak Tours Washington Trips Seattle. They also do half day trips.
For apartments to rent for the week, I would check
VRBO® is Vacation Rentals By Owner. VRBO owners are generally very helpful about answering questions about the area and neighborhood safety. Most suite hotels will be much less like an apartment and more like, well, a suite. I have stayed in hotels all over the city and never felt we went anywhere truly unsafe. Safety precautions are recommended here as in any other major city. We have used Embassy Suites a few times and the two room set up works well with the kids. Bellevue is my favorite area, but it's not really close to everything in Seattle. We have really enjoyed the Inn at the Market (Pike Place), but it may not be suitable for the type of accommodation you are looking for.
For weather, you are probably going to be on the chilly side. Or you may find it a refreshing change from Florida. The average high in Aug is 76. The record high was set 22 years ago at 93.
Food? Our favorites are Le Pichet (great bistro for lunch if you like French food), Pike Place Chowder, Beecher's, Piroshky Piroshky, Metropolitan Grill, Salty's...honestly, there is a lot of good food to be had. There are all kinds of little places to eat in and around Pike Place. You could spend at least half a day poking around the market and find all kinds of things to eat. I like to graze in the market, try little bits from a variety of cuisines. The original Starbucks is down there, if you are into coffee. I personally like Seattle's Best Coffee better and our kids love their Italian Sodas.
You are going to have a fabulous vacation. My fingers are crossed that you have your passports because getting Seattle and Vancouver in one trip will really take things over the top. Vancouver is about a 3 hour drive plus border crossing.