I bought 50 two dollar bills just for dining tips. I usually left two or three per meal. Depending on the service.
My kid is now in the restaurant business, and I can tell you that leaving something really odd like a $2 bill is definitely not appreciated. The reality is they can't do anything with such, and because of it, the $2 bill will just get tossed into a drawer or box.
Leaving a $2 bill, or a $1 coin, is worse than leaving no tip at all, and writing "FU" on the check. You'll be badly remembered by the table help, if you should ever dare to return.
In other words, if you think you're being cute or cleaver with a $2 bill, you're not.