I used to love Dunkin's coffee! McDonald's is good too. Nowadays I find take-out coffee to be too expensive, but maybe this is yet another sage tip in spirit of a past thread (offering to take someone on a date using nearly-expired movie coupons,) as well as trying to seal a deal with someone at Starbucks.
I don't go to Starbucks often, but I can say that for the past 3 years, I've gone at least once a year -- exactly on my birthday.
I'm not into Starbucks coffee but many of my friends and family are. Unless it's changed, you can sign up for their Rewards program, buy gift cards in multi-packs, then give them to your loved ones as gifts.
However, before giving them away, I add the card numbers to my Rewards account. Each time someone uses their card, my account is credited with points. After a while, I might have enough points for a free cup of coffee (sure to impress your date if you offer to "pay" for her.)
And even if you don't rack up enough points, just being part of the Rewards Program (at least for now) means they will load a coupon for a free drink onto your account -- but it can only be used on your actual birthday.
I usually get some unique seasonal flavor or vanilla bean as the old reliable.