The problem isn't the location, it's the company. You've got to navigate the social obligations to avoid
Restaurants: Find ways to bow out of unnecessary meals (e.g., breakfast/brunch can usually be avoided with sleepy/hung-over type excuses), but accept that you're going to be going to some dinners and spending some money. Figure out early whether they're the type to itemize, or just split the bill evenly; nothing sucks worse than limiting yourself to the cheapest food/drink, only to wind up on the hook for an equal share of everyone else's extravagance!
For things like day trips, consider finding alternatives like the ones folks have already suggested, especially if it's something of particular interest to you. Frame it more as you wanting to do something different on your own, as opposed to a money issue. Still might not go over well, but at least you have a better chance of not looking like a party-pooper.