The Price of Food
If you live in a hotel for an extended period of time (which can provide significant career benefits - click on this link for details [1]) the issue of food price and availability is going to concern you.
If you are in a decent hotel you will have a fridge in your room that you can use for your own food. A recent trend downwards in hotel quality has been to use fridges that are stocked with over-priced drinks that have sensors and automatically bill you if you move any of the drinks. A good hotel will have a fridge that either has space for your own food/drink or which allows you to temporarily move their stuff out. If you are staying in a hotel for any period of time and the hotel is not run by robots then you should have the option to negotiate the removal of all the over-priced drinks to provide you space for your own food.
If you have such fridge space then you have good options for making sandwiches - which are cheap and healthy.
In UK hotels (which incidentally tend to not have a fridge in the room if they are affordable) the standard practice is to have breakfast included as part of the hotel fee. If you are flexible about your eating then you can eat a large breakfast and have a minimal lunch to reduce expenses.
Finally you have to consider how much you earn as an hourly rate (after tax) and compare it to the cost of food. For example if dinner at a cheap restaurant costs $10 and you earn $30 per hour after tax then you only need to save 20 minutes of your time by eating at the restaurant (as opposed to making a meal and washing the dishes) to make it economically viable.
I have previously written about the efficiency of work [2]. I think it’s reasonable to assume (in the absence of any formal studies on the topic) that when your efficiency of working decreases due to over-work your enjoyment of your leisure time is also reduced on a per-hour basis (in addition to having less leisure time). I know that some people enjoy cooking and consider it a leisure activity (my sister seems to be one of them [3]). But if cooking isn’t something you enjoy then you will probably feel that eating out is reducing the amount of “work” time and therefore increases the quality of your life and the quality of your work.
Finally for the time spent living in a hotel while searching for work (if you travel to another country without arranging employment first) the main financial factor is not how much you can save money on a per-day basis, but how quickly you can find work. The ability to accept a job offer from any region has the potential to significantly reduce the amount of time taken to find work and thus put you in a better financial position in the long-term. This benefit of living in hotels should significantly outweigh the extra expenses of eating out etc.