One option that is often overlooked is the possibility of staying in an apartment instead of a hotel room. The difference (which is not always reflected in the name) is that a hotel room usually will have a fridge that is mostly filled with over-priced drinks and has no facilities for cooking and often no facilities for cleaning clothes. A recent disappointing trend is of hotels that have a “bar fridge” that is entirely filled with things that you have to pay for which have sensors such that if any of them are moved then you have to pay. This prevents you from moving the rubbish out of the way for the duration of your visit so that you can store your sandwiches there.
An apartment will ideally have a fridge which is entirely empty for you to use for storing food and ingredients for your own cooking (it will have a minimally supplied kitchen). Apartments tend not to have a fry-pan in the kitchen, the reason for this is that they are legally required to have a smoke detector and false-alarms cause lots of problems for everyone (often it starts with an insanely loud alarm in the room which annoys everyone who is in a nearby room). You can expect to have two pots of different sizes and a toaster for your cooking.
If you are after cheap travel then the thing to do is to have cereal for breakfast and sandwiches for lunch. Finding cheap places to have lunch in a new city can take time, and finding cheap places to eat lunch near tourist attractions is almost impossible.
Some apartments have a washing machine and dryer in the room, but it’s quite common to have communal facilities for washing clothes. In any case there will be some option for washing clothes that doesn’t cost an excessive amount of money.
Another significant difference that is commonly seen between apartments and hotels is the layout (which is dictated to a large degree by the size). An apartment may have walls partially or fully separating it into separate rooms. One apartment I stayed in had two separate bedrooms (with doors), a kitchen area, and a lounge/dining area which was separated from the rest of the apartment. That made it possible to have business meetings in the lounge area while someone slept in one of the bedrooms. Another apartment I once stayed in had the bed area partially separated from the lounge area, the wall didn’t extend the full distance but covered enough that a business associate who walked into the lounge probably wouldn’t notice the bed area. There is a significant difference in principle between inviting a business associate to the lounge area of an apartment and inviting them to a hotel room…
Apartments often tend to be more expensive than hotel rooms, they need more space for the kitchen and don’t drive revenue from a mini-bar or a hotel restaurant. One possibility for saving money could be to use some inflatable camping beds to sleep four people in an apartment that is designed for two. They try and discourage this by only having enough cutlery for two people and not having spare blankets, towels, etc (I’m sure that they would bill you extra if they caught you). In contrast hotel rooms often have an over-supply of towels and blankets as it’s easier to just fill every closet with them than to deal with requests from customers at odd times of the night.