Personally, I'm old school and genuinely enjoy dinner dates so I do them on first dates a lot. I'm relaxed and have fun with it so it works. But there are excellent reasons not to, especially if you are on an approach or online hotstreak and are spinning tons of plates.
But if you are trying to keep costs down, I think you are better off avoiding food altogether. Do coffee or meet for a drink instead. It's a win win because it's not expensive, you don't have any major time commitment (you can even do a few of these in one day), and you aren't getting judged from the onset for being a cheapskate. It's been said before that getting guys to spend money on them and jump thru hoops is the goal of female game like sex is the goal of ours. Even chicks that aren't golddiggers are going to take notice when you suggest McDonald's for a date. Why start out like that?
In this particular case, tho, she overplayed her hand and revealed a not so flattering side of herself to you. Doubt you would have gotten an apology had you not gone radio silent. I'd be tempted to next this one but would probably still go out. Just keep your eyes open for other indicators like this.
Gotta admit, if you truly don't care, her reaction to "Chill out, I haven't even seen you naked yet," as someone suggested would be priceless.