I'm not a fan of movies as dates, simply because it doesn't give you much of a chance to interact, unless you are all movie fans and love sitting around and discussing it afterwards.
You didn't say what time of day it was going to be on Saturday, or where you are, but going to a park if the weather is decent is good. Walking and talking can be fun, sitting and watching people go by and chatting as well. Some parks have the possibility to rent bikes and the like.
We have some nice wine-growing areas around us, so a mini wine tour can be fun for us.
Visiting some sort of museum, if it's not too stuffy - we have a great museum like that - the Corning Museum of Glass - cool stuff for artists and geeks alike!
Shopping can be a mixed blessing, especially if some of you aren't really into it.
Sitting in a cafe or coffee shop can be fun, if the weather isn't good. The other benefit is that a lot of coffee shops have those free "what's on locally" papers - you can use that as a basis to discuss something else that the three of you would like to do on a future date.
If you are trying to gauge your relationship with her, then I think time where you can just interact without any pressure would be a good idea.
Most of these ideas can be done on a limited budget.
"Listen, or your tongue will make you deaf." - Native American Proverb