I love when I get to expense things for work. I'm going to 8-10 different cities a year for events, and I try to stay a day extra in each one, at least, to explore on my own. We don't have any sort of per diem, our boss just asks us to be reasonable. I definitely use this as a way to try out some of the more delicious local foods (and craft beers!), without spending too much out of pocket!
The rule is that the company will pay for anything they would have to pay for even if you did not stay, for example rides to/from the airport, doesn't matter if you go on Tuesday or Wednesday, they still would have had to pay. Same thing with meals, they will pay for breakfast, lunch dinner, and any snacks you get on that event day, so I try to get at least one big meal on the work day, along with a few snacks, that can last for a few portions, so I have things to munch on while I am on my exploring day on my own! Have saved a ton of money and explored (ate my way through) some really great cities this year.