A quick note to those a little earlier on in the process: try to come up with 3-4 potential plans before lining up the date… In fact, try to just have 3-4 fun things planned each week, and invite your date along as a first date. Knowing that you were going to do whatever it is anyway might make it seem less special, but especially at the outset of dating women like to feel less preyed upon, and showing enough interest to invite her along like this shows her you're willing to "let her into your world"… And if your world happens to be fun and exciting, she's more likely to want to return later. 😉
That said, a few real basics to get you started:
The Beach Chalet at Ocean Beach is pretty nice for a meal/beer/sunset. A bit cold and breezy, though, so bring a warm coat (to wrap her in?).
A drink after work on the comfy couches of The Press Club just off Market St is a little cozier, and not cheap, per se, but definitely bang for buck a great investment.
Apps and cocktails at the bar at Ozumo on the Embarcadero is, again, not the cheapest, but totally reasonable. Nice if she likes sushi…
Happy Hour at Butter is a little wild perhaps, but the just plain absurdity of the place is fun, and it's loud enough that if you're not a good talker you'll have good excuses to keep it to a minimum.
Me? I like bumming around North Beach at random. It's right on the edge of Chinatown, lots of bars and bookstores, a restaurant for every palate, and yes, even strip clubs. Best grubby pizza is at Golden Boy, and once you're through the line, you can cram up to a bar and eat/talk to your hearts' content. Nice wine bar just across the street…
I could keep going on, but it would help to know a bit more about what you had in mind, and some background… Otherwise you'll just get random opinions. Does she know it's a date? Being Chinese is so irrelevant I won't address it…
Overall, just keep the date fun, and low pressure. Let the atmosphere or activity be your guide, and just enjoy whatever happens. The very worry that you don't want to mess up is often the surest way to make sure you do. 😉
So, where can a lover on a budget take a girl on a first date in San Francisco without needing a government bailout afterward?