In lieu of favors, place a card at every table explaining that you chose to donate money to a charity that has a lot of significance for the both of you. This is such a heartwarming and thoughtful gift, but be really careful when selecting the nonprofit lest you offend someone.
The donation route can be the more budget-friendly option, as you're controlling the amount you're planning on donating. The cards won't cost much, as you can just design and print them out at home. And if you don't want to do the artwork, you can always download a wedding donation favor template, like the one pictured here ($6).