I wish birthday's were simple like they used to be. My mom said when she was a girl, her mom would open the door, call all the neighborhood kids in for some cake, and that was her birthday party!!!!
If I were you, i would do something similiar... invite the girls from your apartment building over for some cake, and to play, and voila! Instant party! I would say to the parents "it's my daughters birthday and we are having cake on __ day at ___ time if you'd like to come!"
for my daughter's summer birthday, we have been reserving a pavillion at a state park (for FREE!!!!). last year, i went to the dollar store and bought the huge bubble wands ($1 eash), they make great bubbles. the kids played on the playground, played with the bubbles, and had some cake. it was perfect.
This year, I found some patterns for some simple paper kites, so I will have the kids decorate the paper, I will turn it into a kite, and they can run around! I'm also going to bring the bubbles again this year since it was fun last year, and again, we have the playground. Simple, fun and cheap!