Since my family lives all up and down the coast, I traveled with Alice by plane a lot when she was little. Since then, there are even more food technologies (and restrictions) and toys but here are a few ideas I found worked really well for us.
If you can, try to plan the flight for a take-off time that corresponds to sleepy parts of the day. This might make them MORE grumpy, but it also means they might just sleep for most or at least part of the journey. That is a very good thing for staving off the boredom that comes with having to sit for too long.
Make it Less Scary:
If this is likely the first flight your child has had that he/she will remember, you'll want to talk about what to expect with him/her before hand. The more knowledge they have about what to expect, the more in control they feel. Speak with your child about the noise and rumbling they are likely to hear, popping ears, and the many cool things you are likely to see at the airport and on the plane. Don't talk about how it might be scary, just talk about it as though it is part of what to expect and be positive about it. For example, "Planes are so big that the engines needed to move them through the air have to be so noisy that people working on the ground have to cover their ears! You won't hear that much noise but we will hear some of it. Maybe you'll even see someone on the ground loading our suitcase into the plane wearing their ear covers." Talk about it in little bits frequently leading right up to the flight.
Give yourself plenty of time:
Don't be in a rush getting to your flight. It will stress you and your little one/ones out and starts every one off on a bad foot and in a bad mood. Instead, give yourself an extra hour or two to "hang out" in the airport. Since you have a walker he/she will probably want to be on the move for much of the day, so let that energy out now. You carry the backpack while you let your little one do the walking (yes, especially if you are the only adult, this is one of the times when checking luggage is probably the more efficient plan). The more walking done now (fun walking that is not rushed), the more physically tired he/she will be and the more likely your little one will be ready to snuggle a bit and read some books.
Plan Ahead with Food:
There are so many wonderful pre-packaged, easy eat foods available these days. Freeze dried fruits are a yummy and relatively healthy way to stave of little tummy rumblings, as are pretzels, veggie chips (some are healthier than others) and basically anything pretty dry. Good old-fashioned Cheerios musn't be forgotten either. In fact, for your 2-3 year olds, The Cheerios Play Book by Lee Wade is a great little board book where kids match up Cheerios to fill in what is missing on the pages to create pictures. Who says playing with your food is rude?
You are well served to bring a new book or two as well as a new toy. These can be offered up as a nice "surprise" when boredom has fully set in and even the most favorite toy or book in your arsenal won't satisfy. You also might find that some of the items I usually include in my "travel basket" for the car are equally nice on the plane.
For the new book, I recommend one with an audio file - this is a likely to be a new thing and although your two-year-old isn't likely to know when to turn the pages to match the story, having something to listen to that ISN'T your voice can be just the novelty he/she needs. Don't worry about it and let your little one turn the pages at his/her own pace as she/he listens. If you have a pre-reader, go ahead and show them how to follow along (most of these audio files have two readings, one that has a sound for when the page gets turned, and then the more advanced version with no signal to turn the page).
My Favorite for the 2-3 year old audio book is, Down on the Farm by Merily Kutner, but a close second - especially for boys is Good Boy Fergus by David Shannon.
My Favorite for the 3-4 year old audio book is, If you Give a Moose a Muffin by Laura Numeroff. Laura Nemeroff has done a number of these chain reaction books. They're all great, I'm really not sure why the moose one is my favorite, it just is.
And for the 4-8 year old I would recommend any of the Skippyjon Jones series by Judy Shachner. They produce giggles and so much fun - especially the versions with an audio file.
We loved our travel aqua doodle, although the pens do require water which means buying water once inside the airport, and having a very skilled hand at pouring, or bringing a small funnel. A Magnadoodle seems like it work about the same as an aquadoodle, but check on whether the magnet and iron filings are going to set off alarms with security or not before you fly.
If you can manage finding a travel sized tube of paint, or have powdered tempura paint, you can do a gallon sized ziploc bag with a piece of paper inside it as a great sensory activity. Put the paper and paint inside the baggie (double bagging isn't a bad idea), lock it shut and then set it on the tray table and let your child push the paint around with his or her hands. Its a great sensory activity.
Bring along a fidget (scroll to about midway through blarticle for a description of fidgets and some ideas of different kinds you can obtain) that is age appropriate and new. You can even make your own.
Have a leap pad, or other computer game type of activity that is still age appropriate.
We also loved our Imagine With Elmo Magnetic "storybook" with its scenery and magnetic outfits to use on Elmo and Abby Cadabby.
There are also so many ways to play movies these days, it shouldn't be too difficult to bring along a favorite movie or two.
Consider your flight an adventure. If you have an upbeat attitude about how cool flying will be and are well prepared, your child/children will feed off your attitude and mood. Talk about everything you see. Make sure to bring a sippy cup or the preschool version with the straws that fold in, any lovey your child is fond of and your favorite book too (just in case someone decides to take a nap). Oh, and I almost forgot, all those extra diapers and wipes - just in case.