Not sure how your PTO runs, but the no budget thing is concerning. I'd try to get more information regarding this, and maybe go to the next meeting and make a motion that the carnival be assigned a budget based on last year's invoices. This may be a bigger problem for us than for you depending on how you're set up, but with my school we aren't allowed to spend anything without either a budget or a vote at a meeting on the expense.
Is your carnival meant to function as a fundraiser, or is it simply a fun activity for the families and you just need to break even? This will determine a lot of the direction that you'll need to take.
What ages are your students? It sounds like maybe you have both primary and secondary students in one school?
For our carnival, which isn't a fundraiser, we separate things into sections. We have one section with games that are appropriate for our youngest students and preschool age kids. This is where our fishing game, a bean bag toss, rubber duck pond, and a wheel of fortune are located. We have a section for the cake/cupcake walk, a section for inflatables, a section for putt putt, and a section for games for our older kids. Those games include a balloon dart game, a tp toss (toss a roll of toilet paper into a toilet seat), a milk bottle game, a basketball shooting game, ring toss, pingpong ball toss, etc. We spread vendors out on the lawn between games as well as placing them in the cafeteria with tables set up for eating. We also have a fire department rep bring a truck and an ambulance for the kids to look at, and a rep from the local police department to do the same.
Most of our games have been made by parent volunteers. Another option is to ask each classroom or grade level to make a game booth. Our booths are constructed with PVC Pipes and curtains. The games themselves usually have a small wooden platform with a bottom and three sides, that sets on a table or rolling cart. The balloon dart game uses a piece of plywood and is separated from the others in its own booth to keep darts from going through the separator curtains and hitting someone in the next booth.
We do everything except for food with tickets, so that the only money that has to change hands for game playing is done in one place, and we use punch cards for prize redemption. The fishing game involves catching fish that are attached to paperclips and have a "point" value to determine the number of punches the child earns to their card for the prize room. Same concept for the wheel of fortune. Playing a game guarantees one punch, winning or partially winning (knocking over one milk bottle as opposed to all of them) gets additional punches. When they're done playing games, the kids bring their punch cards to the prize room for redemption. Inflatables require tickets, but don't earn punches at all.
We manage to put on an awesome non-fundraising carnival for a school population of 630 kids with a budget of $2300. If you need to raise funds there are some good ideas in "Beyond the Bake Sale", which is available pretty inexpensively over on Amazon.
Also, look around for the inflatables. This year we discovered that for $250 we could purchase our own bounce house. We had been renting one for $250 per year, so as long as we get at least a year's use out of it we break even, and if we get more than that we're ahead of where we were. Our local putt putt place agreed to come set up a putt putt game for $250. We pay about $300 for our huge inflatable slide.
Hope some of that helps!
~Lisa