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Unfortunately my suggestions are limited since when I visit, my tourguide keeps kosher...but I have to say Pabla Indian Cuisine makes some realllly good food! It's in a strip mall so it will probably suffice your paper napkin criteria (nice analogy by the way), but either way it's delicious and they have a good lunch buffet.

Hillary
Chew on That

I'm going to suggest Thai House. It's amazing. Ate there every time I was in Vancouver and wanted to get food to go to take home even (but couldn't quite figure it out). Everything that was brought out looked good even those dishes going to other tables and such incredible flavors. I especially loved both their Chili Pepper Fried Rice and Curry Powder Fried Rice. I don't usually like rice much but these were soooo good and so different from any other fried rice I'd had. So much fresher.

Have a wonderful and fun trip (don't miss Stanley Park). :)

Thai Tom in the University District of Seattle
Txori in Belltown

Just north of Seattle (and north Seattle itself) has some restaurants that are cheaper than in the heart of the city. They're more often family-owned and not as flashy, but the food is cozy and the people are fun.
If you feel like swinging up into shoreline: Spiro's pizza/pasta, Kam Rai (Thai, owned by a very sweet man who shares my same birthday!), Chef at Wok (North Seattle, realllly good Chinese), and there are others!
let me know if you're interested in a 15 minute drive up north for good food!

go to pikes place market in seattle and everyone go to different stalls and buy small bits of favorite foods then take it all out on the grass and have a picnic. we did this and it was so good. had smoked salmon, perfectly ripe peaches, russian tea cakes and some splits of wine from the liquor store across the street.
Then just north of vancouver there's a small town? called horseshoe bay. there's a large ferry station there where cars can get on. we found the place by mistake and it was awesome. we had to stay in the fleabag hotel there near the ferry stop but oh well.. we did have one of the very best dinners at a restaurant on the pier. it was october and chilly. they lit the heat lamps and sorry you don't like seafood but we had the crab sampler with dungeness crab, king crab and i don't know what other crab but it was the most awesome dinner we ever found by accident. it was a little pricy, but not outrageous by any means.

Oh, nightmoon reminded me, do definitely go to Pike Street Market. Spend the entire day in the area even. It is worth it to get the perfectly ripe peach, blueberries and cherries (Washington does some wonderful great big ones that should be at their peak then plus you can watch the fish get flung by the Seafood vendor there) and go across the street from the market to get a coffee from the "sort of" original Starbucks location (just cause) then head down just a few doors to Piroshky Piroshky to get a Russian pastry. Those were to die for and you'll probably find the place because of the line starting outside but it's worth it. With a bit of fruit these can make a meal or at least a substantial snack. The potato, onion and cheese and the cheese onion garlic roll are incredible. Then you can get dessert there too (or maybe breakfast for the next day to eat at your leisure before heading out). Apparently it's Zagat rated and won number 8 on the best of for Bakery at Seattle CitySearch (seems to be several others on that list at the Market too). There's also another Russian restaurant in the Market area that's supposed to be very inexpensive (less than $10) called, Cafe Yarmarka which I found looking up the first place. I've never been but it has great reviews on the web and would be a different sort of experience for perogies and stuffed cabbage.

I'd also say if anyone does want some fish then Ivar's Fish Bar which is on the waterfront behind Pike Street Market (next to their "Acres of Clams" location) is the place to go. It's basically a Seattle institution and worth it for the waterfront view and people watching. Those who don't want seafood can eat some good fries and coleslaw (though they have chicken too -- there are other places in the area to catch a different bite though).

Then make sure to hit Granville Island for a day in Vancouver. I love that place and it has a Public Market too for great inexpensive eating with several vendors so everyone can get just what they want whether to eat inside or take out for a picnic. You can take a Foot Ferry (Aquabus) there, say from the Science World (taking the SkyTrain to there) or just take a tour of False Creek (it's fun and worth it). We discovered the joys of eating at the Public Market when our hotel charged us the full price on our hotel (5 days) every single day we were there causing the credit card to go into shock and all we had was about $20 in cash to eat with. It's one of my favorite memories.

How 'bout specific recs for Japanese noodle houses? I know the food court at Uwajimaya has options, but I was hoping for some stellar ramen in some little hole-in-the-wall Japanese shop.

Hey!
You have many restaurants to eat there... check out this site for more information.. www.yummyuck.com.. you can also read reviews, other people's experience and price structure without steppin in to it.