The absolute best money saving thing you can do while traveling (besides having me plan your trip!) is to grocery shop!
When I travel somewhere, I like to pretend like I live there. Do the people who live in Paris eat out for every single meal? I'm pretty sure they don't.
Some of my favorite travel memories include traipsing around the grocery store trying to figure out what to buy and decoding packages in different languages. It's just fun to pick out weird mustard and try new candy bars. Grocery shopping makes me feel like I am actually experiencing the country rather than just being a tourist.
This is not to say you can't go out to eat. Honestly, when we were in Italy, we ate at restaurants twice a day. I had a friend who went to four pizza places in one day. Goals. But in Norway? No offense to Norway, but their restaurant food is overpriced and not super delicious unless you like very salty fish. Their chips and bread though? Unforgettable. I miss those blue Norwegian Doritos. Also they happen to have a scary looking do-it-yourself bread slicer in each of their stores. We figured out how to work it and still managed to keep all of our digits, though the directions were not in English.
Here is a sample list of things we buy when we touch down in a new country: bread, some sort of meat, cheese, mustard, Nutella, fruit, cereal, milk, plastic bowls and spoons, baggies. We bring along a little lunch bag and always have some food to eat on our person. This keeps us from getting hangry or getting stuck at an overpriced tourist trap restaurant. It encourages us to seek out worthwhile food instead of eating for convenience.
This also helps me to not have travel scurvy. I am not talking about the ten pounds you gain while traveling, (can't help you there) but the feeling of being constantly stuffed and not eating fruit or veggies. Plus, picnics! The only thing to make a beautiful sight better is to have food to enjoy while viewing it.