Thank you for your question! It is definitely one of those “million dollar” question that many people are curious about.
As a gentleman, it definitely leaves a positive impression on the lady when you offer to pick up the tab. However, a meal or a date is not just about picking up the tab. Gentlemanly gestures like pulling out the chair for the lady, taking the initiative to pour her a glass of water and being observant of her needs during the meal will score you brownie points as well.
If the lady offers to split the bill with you, be appreciative but gently decline her invitation. Usually the lady would graciously accept the treat without further protests. Of course, you can suggest to the lady to pay for coffee or desserts after the meal, so that you get to spend more time getting to know her better too!