If you are trying to keep the budget down, you can have the party after noon, perhaps 1:30 p.m., which allows enough time to have lunch. Then write a little note in the invitation to "Join us for cake and ice cream..."
We had a local pizza place called Graziano’s Pizza that had a small arcade, they did parties which were very reasonable. Sadly I just looked and they have closed.
You will just have to call around to see what the rates are. At 8 years old, I would suggest, laser tag, the endless trampoline places, or take them on a family trip.
See if you can find a place like that to do the party.