We bring a water bottle. It can easily be filled up - in most European air ports there are filling stations on the inside of security. So just bring an empty bottle.
In countries where buying water is necessary, look for the affordable water that the locals buy - buy in bulk and fill your bottle.
We bring snacks and packed lunch. For longer travel and on the go, it is really nice to have some nuts, hard bread or similar options on hand. Often bring it just in case - with delayed travel or long time to a meal it could save your low bloodsugar situations and keep up the good mood!
Bring a packed lunch from home. If you want it to stay fresh longer - you can make sandwiches with cheese, meats and similar and pop it in the freezer. Take them from the freezer when you leave and it will be thawed and fresh when you need it. Greens should normally not be included in the freezer as they will wilt, but you can bring them separately from the fridge. Last day we also make the leftovers into sandwiches like this. If you have greens, eggs over you can make an omelette for your lunches.
For activities - search “free things to do in :location:” and you might get many tips on fun things you haven’t thought of.
See the area.
Learn the language and give yourself little tasks. Saying hello, thank you and good bye, learn to ask for a bag or a bus ticket. Learning outcome and so much more fun to be a part of the community.
Look up! Lot’s of great architecture!
Church services can offer nice musical and cultural experiences.
Check if it is special days and celebrations. There could be public celebrations, parades and similar not to be missed - true cultural immersions.
Museums might have certain days with free admission (sometimes these occur only off season). Or splash out and avoid those dates, as they can be busy. 
Check out if there are something you can contribute to as a volunteer. Sometimes you can contribute to local charities, animal rescues, nature preservation or similar. Great experience, get connected with the community and make memories making an impact - make the location you visited just a little better after they had a visit from you!
It could just be an easy thing like bringing a bag and pick some litter (or
), sweeping or visiting a charity contributing, buying a coffee to support or similar.
Use public transport to sightsee. Getting a bus card is often quite affordable. Make it more than transportation - make it the experience! See the surroundings, the nature, how people live, how people interact. I’m from an introvert country - it is really special to experience how in some countries all passengers from the back door would say “have a nice day!” to the driver up front before they go off. Something to inspire us to be more attentive to one another.