Well, I have only lived here for just under a year. I don't know of many places for parties (low cost). Jump Zone and Little Gym (both in the Moore area) are awesome for kids of all ages and I believe they both do parties.
Could you ask a family member to donate their house? We had our daughter's at my Grannie's house due to the lack of room at home and it was fine. Nothing spectacular, just cake and gifts and a lot of friends and family to celebrate.
As for first birthday parties, breathe! Don't get caught up in the hype and the show. Make it as much about your new baby as you can. Relax, have fun and expect a mess! Enjoy it, because it only happens once. Before you know it, he'll be jumping and growling and even keeping the majority of his food on his plate. ;)