DottyG - Yes I am one of the people involved. I was trying to keep it as objective as possible so I left out some of my thought processes that I thought would tip it off that I was Sara. I'm sorry if I left the impression as a result of those omissions that this was a big problem - it is not in any way a problem between myself and Vicky who I consider to be one of my closest friends and with whom I spent an enjoyable evening with after the dinner misunderstanding studying and watching our weekly show. I have not and have no plans to mention this to anyone in my real life - I just posted here because this had never happened to me before and I was trying to figure out where the breakdown happened and how much of it was because of me. When I did call Vicky upon getting home, we barely even talked about what happened, just a general "What happened to you?" from both of us to figure it out and then we switched to arranging our study plans. She did say when she came that she was sorry that she hadn't just come to the restaurant and that she didn't know what she had been thinking, just driving around the way she did. I told her it wasn't a big deal, just a fluke that could have been avoided if I had remembered my phone. (Though as Toots pointed out - it all would have been nipped in the bud if I'd been clearer in the planning)
When I said I was over it but frustrated, I was referring to what I consider a human reaction to finding that one's plans for fun have come to naught in a time consuming and a little stressful way when one is very very hungry - after I ate dinner and relaxed the frustration abated. Honestly, Vicky would have to do something seriously seriously wrong for it to have any lasting effect on our friendship.
As to why I didn't just leave to go to her house instead of waiting? When I walked into the restaurant, I thought I had texted Vicky that we should "meet there" - so I figured she'd show up there eventually either because of the text or if worse came to worse, I genuinely thought she'd come to the restaurant when I didn't show up at her house within 10 minutes or so of 7. I also had already sat down, ordered a drink, marked my menu (you check what you want and they pick it up), and used the hand towel. I will admit that I am not the most self confident when it comes to unfamiliar situations so I felt uncomfortable asking for a bill with only a soda on it after all that. I was also self conscious because waiters kept stopping at my table and then doing that double take and walking away when they realized that I was still waiting for someone.
When I first got there, there wasn't a clock that I could see (I later discovered the taco on the wall was a clock, not just a piece of art) and wasn't sure how long I had waited - I did entertain myself by trying to guess what time it was based on the dramatic progress of a Bones episode that they were playing. I also wondered if maybe Vicky had mixed up the times and thought we were meeting at 7:30 since that was originally what time we were going to study together before I suggested getting dinner first. After I realized that 7:30 had passed, I went ahead and ordered to go. I vaguely thought about stopping at Vicky's house on my way out, but when her car wasn't by her house, I thought maybe she'd be waiting outside of my place, so I went home and I suppose I must have just missed her.
So yeah, not my finest night in terms of common sense - In my defense, it is finals time, so I'm not exactly firing on all cylinders

Thank you all for your take on things!