Everyone is different when it comes to spending money, some people may prefer to take just their card or vice-versa with cash (which is absolutely fine) however in many places this may hinder your accessibility to experiences. All of my advice is based on my experiences in different countries/continents and may differ to where you are going.
I do not usually book my trip depending on how expensive the place is said to be however it is definitely something to take into consideration, as the last thing you want is stressing before you go that you won't be able to get by out there. When it comes to a European city break I follow a routine when it comes to spending money, regardless of the destination; a few things to take into consideration is personally I don't drink the tap water anywhere I go therefore paying for water is accounted for in my budget. Not only this but I pre-book all of my activities and excursions on Get Your Guide, this is mainly because I believe you get a better price online and you can ensure you get the space you would like, as well as the fact I won't have to worry about not having enough money left for the activities I would like to do. Also, when I'm on holiday I tend to eat out for all meals, as I am not a big fan of a continental breakfast and usually stay in hotels not apartments so have no means to cook. Note: Nothing beats eating on the main square of the city you are visiting and watching the world go by.
A true example of my budget would be: a 3-night city break with an early flight on the way there and a late flight on the way back means I have 4 full days to budget for. I would allow £60 for each of the days I arrive and leave (as long as I have pre-payed for a transfer and accounted for tourist tax) because I will likely need two meals, and transportation around the city. On the last day I tend to buy souvenirs for my family, but usually I would have money left over from the middle days for this. Then the two non-flying days I would allow £100 a day, this may or may not seem a lot but it has always worked for me. This money would be enough for three meals (one from a street market/cheaper restaurant or cafe), public transportation around the city and a drink in the evening. All of this money would be cash in the local currency, but I recommend always having emergency cash on your card. Emergency money doesn't have to be for an awful event occurring, it could simply be that you have come across an attraction or tour you hadn't seen online, a restaurant that doesn't take cash or even that you overspent the day before. But taking cash with you is definitely essential as many street markets and local hotspots may not take card and you don't want to miss any opportunities.
Obviously this routine won't be suitable for all destinations, I was extremely naive when I visited New York to the point where I had to go into my overdraft just to eat! I had budgeted £200 a day for two people and ended up spending up to £50 over budget every day! I blame this on the shopping though as usually on a city-break I wouldn't spend my money in the chain stores that have exactly the same lines in the UK but the shops in New York are irresistible. So make sure you do your research on exact destinations that you suspect may be more expensive.
Another thought to take into consideration is the different types of holidays available, I struggle more with budgeting for summer beach holidays as it is often only when you get to a resort when you decide whether you will stay in or eat out. But a few tips would be: pre-book excursions and waterspouts and take snorkels, goggles and beach shoes with you, as in smaller beach destinations the local shops/stalls can be very overpriced due to the convenience and lack of competitors. My main struggle when considering money on summer holidays is that if I end up booking an all-inclusive, I without a doubt will miss one or two meals a day from being busy outside of the resort. If you are leaning towards an action-packed, exploring summer holiday then try avoiding all-inclusive but I may be biased because (in my opinion) it takes away all the fun of being abroad as you can lose the local vibe from being surrounded constantly by other tourists. For reference, in destinations such as Greece in a half-board or self-catering booking, I would allow £60 per day for food, water and snacks each.
Obviously it goes without saying that if you are on a small, tight budget you can easily shop at local supermarkets and make meals yourself while taking public transport or walking to the sights. It really is down to personal preference and how you decide to holiday.