The cheapest and best party I ever threw for my daughter was a mall scavenger hunt party. I was sceptical at first because I didn't want 12 year olds running around the mall, so I made the rules for the game and each team would lose points if they didn't follow the rules. They included no running, always being polite and respectful, etc. The team would lose points if they did not follow the rules and the Personal Shopper was responsible for them.
My DD invited 6 friends + DD = 7 girls. 2 girls per team and my DD rotated between teams for each challenge.
I had my mom, my sister, my 20 yo niece and a friend help me. Each team had a "personal shopper" (a.k.a.: chaperone). The Personal Shopper kept score for that team.
They had 3 challenges to meet and 20 min to complete each one.
Each challange included 10 items to complete or get and the Personal Shopper used their cell phone to take any pictures for proof.
In between each challange they had to meet back in the food court. After challange #1, they ate pizza. After challange #2, they had cake. After challange #3, they watched DD open presents and we announced the winners of the scavenger hunt (they won $5 Starbucks Gift Cards each).
All told, it cost me about $100, half of which was the pizza. If you did just cake and drinks, it would be a lot less.
The invitations were designed to look like a credit card offer you would get in the mail. I even laminated the credit card and stuck it on the paper with rubber cement to easily peel off. The credit card included the invite's name and party info, but looked like a credit card.
Do a google search on a mall scavenger hunt to get ideas for the challanges. Each challange included $3 and instructions to either purchase their personal shopper their favorite coffee, buy the ugliest pair of socks for the birthday girl or purchase the best gift you can for $3.
Several of my DD's friends even copied the idea and had Mall scavenger hunt parties through the following year! It took a lot of planning, but was LOTS of fun!