While I'm neither single, nor a lady, I can say that when I was dating I found many frugal but fun date ideas. At the time the frugality of them was actually a secondary or tertiary concern, and the primary reason for them was because I didn't like the traditional dating activities (dinner and a movie, going to a bar, etc.) and wanted to find something that I enjoy.
What I found somewhat successful was this:
-Get on a site like Plenty of Fish and write up an honest/accurate profile, describing your interests, life goals, etc. Don't be too serious and throw in lots of your own brand of humour, but don't lie to make yourself look "better" as this will make things more difficult. You are trying to find someone who appreciates your qualities so there is no point in trying to hide them (though do try to pick the better ones to show off first, and start to introduce your annoying quirks a little later in the process).
-Look for ladies with similar interests and outlook on life. If your goal is to travel the world, don't message people who say they want to settle down and raise a 4 child family. If your main interests are hiking and mountain biking, don't message people who say they enjoy going to the club with their friends. Make sure you pay attention to everything in their profile and not just their written description - lots of people say they like hiking/camping for some reason when all of their profile pictures show an unfit person wearing lots of make up getting drunk at the club (as an example).
-Send messages to people you found interesting. Write your message well (with proper spelling and grammar, not with msn/text speak), introducing yourself and talking a little about what caught your eye about them. Suggest getting together to chat over one of the activities you both like to do, but choose something that is non-committal and easy for both of you to duck out of. For example, if you both enjoy hiking suggest going for a walk together, but maybe don't pick a 20 mile climb way out of the city for the first date - just a couple mile nature walk close to amenities will be good for an introduction, and if things go well you can extend it from there.
-Don't be upset when you don't hear back from people. Although two people may seem compatible on paper, not everyone clicks. I would say if you write your messages well, you can expect a reply from maybe one in five sent. Of those only a few will want to meet you after chatting for a bit, and of those only some will click.
Anyway, that's my take on it. I didn't mean to write a "dating guide" as that's probably not what your looking for (and I'm far from an expert at it anyway).
TL;DR: Look on free dating sites for people with similar goals/interests, propose cheap/interesting activities for dates that you both do anyway, don't get hung up if things don't work out.