When our kids were little, we had a travel bingo game - it had little windows you slid closed over the item once you sighted it so there were no chips or bingo pieces to deal with. There's probably an electronic version now. If not, low tech still works! It's great for kids who don't read or know their numbers - it just has pictures or silhouettes of common highway items - bridge, motorcycle, tractor trailer, speed limit sign, etc.
We also had a small box of "car only" toys that never came into the house, but were taken into restaurants for idling away the time while waiting for the food to come. We used those little wooden carved games with the golf tees as markers - they could be used in all the enclosed games, like Tic-Tac-Toe and other simple classic games. So I'd suggest you buy a few SMALL toys and special things just for this trip, and dole them out one at a time.
Go to the public library and see what they have in the CD department - you can borrow a bunch of things for a week. Playing sing-along CDs is a great way to involve the whole family - there are familiar tunes, American classics that every child should know (when I was teaching music, I was appalled at how many kids had never learned "Baby Beluga" or "Oh Susannah"!!), and many are complete with finger play activities that can be so much fun and really pass the time. I know a lot of cars have DVD players or people use portable ones, but to me, kids miss the experience of enjoying the travel, the sights and (gasp!) their parents!! While you're at the library, look for an old book of travel games - the stuff everyone played in the car before they had electronics. These are new and exciting to today's kids, and they cost you nothing!! At 4, you have to distract and divert - you can't just talk them out of being impatient. But turning it into an adventure is a great stress-reducer. My parents drove us from NY to Texas over 4 days. We occupied ourselves!
Stop a few times at rest areas and walk around/stretch. If you would feel better with a "kiddie leash", get one! Beware that the big plazas that have a gas station, a McDonald's, a pizza place etc. often have decent and clean rest rooms, but they also have strategically-positioned touristy gift shops with all the expensive stuff at kid-eye-level! You don't want these pit stops to turn into the activity and money pit of the day!
Take a few snacks, a jug of water you just use for washing up sticky fingers (we always took a bucket or a big plastic container to catch the rinse water, then dumped it at the next rest stop), some wet wipes, and some bottles with built-in straws for our own water & drinks (you don't want juice boxes in the car!). Take a few extra plastic grocery bags for trash, then tie them up and dispose of them at any rest stop. Have a hand towel and maybe an old beach towel. We even - I kid you not - took the little potty seat with us: "Mom I have to go NOW" is pretty frustrating when you're on the interstate and not near an exit! But we could always pull over on a wide shoulder and make a stop as needed. We put a plastic bag liner in the potty and kept extras on hand. See note above about old beach towel too!
It rains in Seattle - so get a few $1 ponchos at the dollar store or in the camping area of the bigger stores. They fit well over a stroller or you can cut one down to child size. And get a couple of collapsible umbrellas with loop handles that can be slung over the stroller handle or stuck in the mesh pocket. Life in Seattle doesn't stop just because it rains.
Since you will have your car, I'd put a decent sized cooler in the car where you can reach it, and not plan on taking a heavy cooler with you in the stroller. If you can find a soft-sided one that collapses, that's easier. We have one that's a padded cube shape with a strap on it, and it goes everywhere with us. It can sling on the back of a stroller or be carried like a shoulder bag. We use one blue ice block that can be refrozen in a hotel room fridge - if you aren't requesting a fridge, think about doing so! You might also take along a small step stool to help your son reach the toilet and the sink in the hotel room. Bring one or two small, new tub toys and maybe a small bottle of bath bubbles. Get the smallest possible container of dishwashing liquid to wash out your cups and containers, and bring an extra dish towel in case the hotel doesn't give you a lot of hand towels. You'll need one for a dish "drainer" anyway!
The 3 wheeled jog stroller is great for outdoor trips like a zoo. I'd take (or borrow) an umbrella stroller for indoor museums - there are crowds, and kids like to jump up and run around to look at exhibits (a good thing) and then one parent is stuck maneuvering the big stroller through crowds and onto elevators, which is a nuisance for everyone. Many attractions allow you to bring in your own food and eat at the public dining areas. Museum/zoo food is expensive and lines can be long - yes, it's a profit center for them, but they also seem to know that many people have food sensitivities, and they are used to hosting school field trips where every child and teacher brings a lunch from home. Remember that the idea of a museum is great for a kid, but that he's likely to have a limited attention span and tire out quickly. Be prepared to leave early and just go have fun. That's where the discounted admission pass can be such a blessing - you don't feel you've invested so much money and then he's done in an hour. Also, museums also can have outdoor parks or be near them - so don't be afraid to leave for a little bit and then get readmitted with your hand stamp.
Look into memberships you might already have for reduced admission to attractions. For example, we have a number of museums that accept each other's memberships - so if there is something in your area that you already belong to (or would like to), see if they have reciprocal free or reduced admission deals with other museums around the country. If you are a AAA member, see what they have for discounts, either by presenting your membership card or by using a discount coupon they have for areas all over the country. They also have a free travel service - we think of AAA for emergency towing only, but they have many other services.
So the idea is to have extra things in the car, but not always be hauling them around with you. Take more than you think you need and then you won't have to spent vacation time searching out stuff. Borrow what you don't think you'll need going forward, or at least to try it out to see if it's something you want to invest in!