Why not try to find free or low-cost activities?
I'm a huge fan of going to free concerts in parks, picnics, renting a movie (or watching one someone already owns) and staying in, local comedy clubs or something of that variety, etc.
I personally hate having other people pay for me unless I've known them for a while and feel like it's fair (as in, both of us pay for things or provide each other with meals or whatever at random, without really keeping track). It makes me feel uncomfortable to think of one person always taking the responsibility for our activities together - whether it be financial or the planning aspect. So, when I first start dating someone, before I feel confident that the relationship is going to last long enough to be mutually beneficial, I try to keep the activities low-cost so that if he/she insists on paying, I don't feel guilty about it. It also keeps me from stretching the budget if he/she agrees to my preference that we go dutch. lol
Most people are pretty understanding that finances get tough sometimes. I'm sure if you're just honest with her that you don't really have the money to be doing fancy dates often, she will understand. If she's anything like me, she'll love the more relaxed, low-key things just as much. It's the time together that counts IMO.