"Foot the bill" is informal, but also has the nuance that you are taking responsibility for the bill, despite the fact that there are other people who might also take responsibility for the bill, and usually this is not used in relation to restaurant visits, but rather in paying for a larger item of expense, such as construction works or university tuition fees or compensation for injury.
For example, I could go to eat alone at a restaurant and pay the bill, but I would not speak about footing the bill in that situation. Maybe if I go to the restaurant with a group of friends I might speak about offering to foot the bill, meaning that I would pay for everyone. However suppose I own a business and my business partner drives his lorry into someone's house by accident, causing damage which is expensive to repair. Perhaps in order to avoid involving the insurance company, I could offer to foot the bill. Or someone's parents could end up footing the bill for their university education.