Personally, 2 year olds aren't going to remember very much about a birthday. My daughter will be 2 next week. We are having a small party at home with a few friends and our family because it is also her brothers (6) birthday. I will buy a grocery store cake for everyone and make her a special cupcake.
If you really want to go somewhere inexpensive. My kids have a blast at the train play area in the mall near target and then go get ice cream or slurpees or something fun as a treat to eat. let your two year old play for an extra long time running around and then get a little messy with the icecream or other treat.... take some fun pics and call it a great little birthday celebration...