Historically, I've snagged some very nice goodie items when I see some sale during the year...and stash it away until bday season. I know, this doesn't work well on short notice
but here are few places to try if you have 1-~2wks for shipping to arrive:
Dig around on Meritline's "Bargain Center" tab. Free shipping and the more you buy, the cheaper the item becomes. I've given these pig-shaped LED flashlights in the past, huge hit (they were cheaper previously, but come down to ~$3.60 incl tax shipping and no driving around, if it is your only item, etc)
I've also got great deals (past) on good-sized art kits and large all-wooden domino sets for $1 here.
Halo Heaven is awesome awesome awesome if you are open to even a smidge of girlie girlie stuff. Awesome prices, lots of retail places buy from them and then mark up the price. Catch is you need to spend $20 for free shipping. They have halos with ribbons (many colors), wands (frilly or with things like butterflies), butterfly wings, etc, etc. Some gender neutral stuff like capes. They have hair clips with bows, animal print bows, flowers, butterflies and insects (I've bought the hairclips and bows separate and had girls make their own barrettes to take home...VERY cheap, VERY easy and a year later, I still see girls at school wearing the animal-print barrettes they made at DD's party. If you get the "bow" style, just slip the alligator clip under the center part, no glue needed). Dig around on the website...lots of girlie girlie stuff, but not all. Shipping is usually ~1wk. All the prices are unbelievably awesome:
If you need something faster, spend some time in Michael's craft store looking in their sale bins. They usually have things like wooden animals/dolls/trucks that are outlined and stand up with a little stand, they come with markers to decorate...or some other mini-craft kit.
Something I always wanted to give but was too cheap and I could never find a good deal was to give just Madlibs and a pencil. They have "junior" madlibs for younger kids where you don't have to know sentence parts, you just create the funny stories using lists of words. Something like thishttp://www.amazon.com/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=junior+madlibs
And, I know you said "no food" but several times we've gotten a gift certificate for a scoop of icecream/waterice at a nearby shop. Love this -- fun for the kids to redeem and totally consumable! (Unfortunately not a great choice for my winter bday kids!).
***edit: Just saw this: zhu zhu hamster for $3 shipped (5 cent flat rate shipping with code MY5CENT, batteries included). Again, I've gotten them for as low as $1, but not bad for short notice and a single goodie item and kids still love them:http://www.shopko.com/search?q=zhu&commit=&s=sale_price%3Aasc***
PS. Congrats on finishing your doctorate!! I'm soooo impressed that you did this as a parent, especially a single parent! I would have never been able to do mine, or my postdoc for that matter, as a parent!!! Wowie!!!