The trick nobody seems to mention is doing a "station party" at home where you rotate through 3-4 simple activities instead of one big event. I did this for my daughter's party last summer and it kept everyone engaged without needing to rent anything or go anywhere. Set up a craft corner (decorate your own crown or mask with dollar store supplies), a games station (relay races, musical chairs, Simon Says - free classics), a snack/cake zone, and maybe a water balloon toss if it's warm enough. Kids that age don't need fancy entertainment, they just want to feel like something special is happening. You can theme it around whatever they're into - superheroes, dinosaurs, whatever - just by using colored paper and markers for decorations.
The food is where you can actually save money without it feeling cheap. Make cupcakes instead of a cake (easier, less intimidating, and you can personalize each one), do a taco bar or hotdog station where kids build their own, or just go simple with pizza and sides. Skip the elaborate goodie bags - honestly a couple of stickers, a small toy from the dollar store, and a homemade treat in a paper bag feels just as exciting to a 6-year-old. I've found they remember the *experience* with their friends way more than the stuff they went home with.