Just an idea but it worked for me. I had the party at home and hired a professional actor out of the yellow pages under entertainers. Had him dress up as Batman. Sent out the invitations saying that Batman would be making a personal appearance and costumes were welcome. Mind you, I think it was the last yr of pre-school so they were all about 4/5. But every kid in the class tortured their parents to come. And I do mean torture. We had a blizzard that day and parents had to drive their kids miles and miles in a blizzard. LOL
The point being that doing it outside the house is typically to get them to come to the attraction, video games, etc. I saved a lot of money by bringing the attraction to my house and so had about 25 kids without breaking the bank or dealing with which kids were or weren't invited.
If you can find something interesting enough for that age you still may be able to do it at home. It's finding something you can afford that they want to see. There are science presenters, crafters, clowns, characters, dance instructors, pro make up artists, gymnastics people, etc, etc that will come to your house. If you have willing friends and can get creative you might be able to do it cheaply. The key is what they'll come for. And you can do it to appeal to multiple interests. eg in the invite say it's unlimited pizza, ice cream sundae bar, take-home craft project specifying something they might want, entertainer, major prize for winning game, etc, etc. And the game could be some sport they all play like shooting soccer ball into goal. Whoever get the most goals with 10 tries past your adult goaltender friend wins the prize.
To do the out of the house thing cheaply you could do the same thing at a park. Then include more sports with prizes for sports games.
Many places like the YMCA rent out the pool. Town rec depts often rent out their facilities too. Condo assoc that has a big room may rent it out. And if you don't belong to any of these beg a friend who does to rent it for you. Again, eliminates the per child charge and if it's something interesting like a gymnastics room, a pool in winter, a basketball court, they'll come. Sometimes the fees to do this are huge and sometimes not.
Doing an at home carnival isn't a bad idea either. You can either make the games or borrow them from a church or school that has them in a closet for their annual event....the attraction is the prizes which you tell them up front what those prizes will be.
Remember that you can rent anything. Could be a huge outdoor inflated ball pit, a pony, arcade games, etc. It's just a matter of space and money.
You need to seriously think about what your friends and family can do. Mine has been to horseback riding parties if you have a friend with a horse. A doctor who'll take them on a tour of the hospital and let them play with baking soda and vinegar in a lab. A friend who is a mechanic and will let them play with the engine of a junk car, spray paint an old car, etc.
You'll get a lot of kids there because their parents will force them if you can get a pro to help them with a HW project, science fair project, etc. So anything they have to do for school that a pro will help them do.