you want to make sure she is comfortable with the exchange in public.  And GiamarieLynn's rose is also a good idea, as long as she is not allergic to them.

I would either meet initially at my place or hers and do it then, or if that wasn't convenient, I would wait until we were in a private setting.

I prefer the gift box because it can be easily tucked into my handbag, but neither will draw much attention. Besides, a gentleman giving a lady a gift box/bag or card (unless it's literally bulging with cash) isn't going to raise any eyebrows. You don't stand out as much as you might feel you do, and no maitre d' or server will risk pissing off paying customers by insinuating you're anything but a perfectly innocent couple.

I think it's easier and more pleasant to meet in the room first so as not to worry about any of that, but you and your lady might feel otherwise.