The word everyone is thinking of, but nobody has said is "utility". A "util" is a measurement (like an inch or a pound) that measures how useful you find something. Usually it is measured in "utils per dollar." Everyone finds utility in different places. If you hate hot dogs, then even though they are cheap, you don't find much utility there. If you're starving, haven't eaten for days, that hot dog would suddenly be PACKED with utility for you... the first would be FULL of utility, the second a little less, the third even less, etc.
Most of the people on the budget boards find utility in the feeling of monetary security. We find value in knowing we have a bit "tucked away". We value the peace of mind that gives us. We find more utility in feeling secure than we would in "blowing" that money on something... but, that said, we can also feel utility using the money for something we have saved for. But it's a balance. I could blow all my savings for that big trip abroad tomorrow, but I would not get much utility from it because I'd be fretting about my lost security, plus my children are too young to fully "get" the experience. When we do go, I want them to be old enough, and I want to pay cash so I can spend the time getting maximum utility from my dollars.
We all experience utility, but most people haven't learned the idea of what it actually is (it's an economics term, btw)
Americans, as a whole, are socialized to find pleasure (utility) in getting "deals." I saw a man at the grocery store on Sunday, pointing out the yogurt to his little girl, about 3 or 4, and saying "it's on sale!" He didn't seem to care whether it was the kind she wanted or even if it was the best price overall, he was unintentionally training this child to get excited every time she sees a little yellow sign on a shelf. Lots of people find utility in the feeling of getting a good deal, and don't even realize why. That's why they buy "junk" they don't need.
It sounds like your friend finds utility in getting a good deal, but you feel that she does not care much if it is at the expense of others. My father-in-law does this a lot. My in-laws talk (complain) a lot about the price of everything, but that said, they go out to eat A LOT. Once they're there, they'll both order water-with-lemon, usually split an entree, and their tips are a frequent source of embarrassment for those of us dragged along. When we go along, I order what I want, try to split the check if possible, and if they "insist" on paying, I shrug it off and refuse to feel guilty. I frequently add to the tip until it's an amount that I feel is appropriate for the service we received, with a bonus if FIL was a total PitA while we were there, and call it all good. I do that because for me, the utility in a meal out comes from me not having to cook and clean and the experience of quality time with my family. My FIL being a tightwad can ruin that for me and take away my utility, if I let it, so I have learned not to.
If your friend's habits really bother you, then you are allowing her actions to negatively affect your utility. But realize that your actions probably seem strange to HER and reduce HER utility in the time together. This is one of many reasons friends drift apart over time... your time spent together becomes less and less enjoyable (you don't have utility from that time.) So the trick is to find the middle ground, as a PP already said. What activities hold utility for you both?
Example-since this is a Disney forum. People here really like Disney. And people on this sub-forum like a good deal. So people here find utility in visiting Disney for various reasons, and find extra utility in doing it in a way that fits their values. You want to RUIN a trip for most of us, come along with minimal preparations. Buy everything in the parks and then complain about the cost, complain about the lines, talk about how long you're going to be paying the credit card bill for this meal that you don't even really like... and don't forget to constantly mention how you don't even LIKE Disney stuff... you get the point... It is very possible for one person to completely drain the fun (utility) out of someone else's day-- if we let them.
In your case, your friend sounds like she finds utility in hanging on to her money, but she does it in such a way that makes the eating-out experience unpleasant for you. My question is, which one of you says "Let's go out to eat?"