Anywhere local you can take yard waste, ie branches, bush trimmings etc? I would burn it but can't have a good ole' burn spot in the yard right now.
Compost it? Got a neighbor with a brush chipper? Make a pile add some left overs from the kitchen (No meat, no dairy), add water and watch it break down. In this heat it'll take no time. Just an option.
The county landfill in Smithfield. We've taken loads of stuff there and never cost anymore than $5. But if you have a sticker to haul your own trash you can take yard waste to the landfill for no additional charge. Another option is the Junk- b- gone guy (919) 650-9224 he's hauled for us at fairly reasonable rate.