Bit of an older thread now, but responding in case this is still helpful - I keep a box in the closet of $1 or less gift items for kids. I buy extra and add to it when I find something great, and pack a gift right from the closet as needed. My kid's gift budget is under $10, but most often about $5.
From the dollar store or Target dollar spot (which now has lots of $3 and $5 things too so be careful): kid band aids with cartoon characters on them, bubbles, crayons (check the grocery/home store for these too - I got a bunch of Crayola crayons from Fred Meyer a few years ago for .30 a box), stickers, sidewalk chalk, coloring book, glitter glue (for an older kid who will use it carefully), rainbow popsicle sticks, pipe cleaners, craft pompoms, finger paint, construction paper, ball, balloons or water balloons for an older kid, inflatable pool ring, pinwheel, etc.
For wrapping, I skip the card (add a diy one if you want, but cards cost money and kids don't care). I have a small stash of gift wrap bought on sale after Christmas - there is usually lots of paper that doesn't look Christmas-y in blues and other colors, or with kids cartoon characters on them, as well as tissue paper, boxes and bags. For a spring/summer birthday, I pack the gift into a $1 bucket and shovel set from target with some tissue paper.
A dollar store gift basket won't look like you spent $30 the way happening to score some toy on a major markdown will, if you're trying to impress, but every time I have gifted one of these, the kid has been very excited about it and starts playing with the stuff right away. Bonus for the parents - most of the items get used up, so you aren't adding clutter to their lives.