Transportation to/from the location. Compare bus, train, plane. If you're in Germany, consider a BahnCard (but it automatically renews every year, so make sure to send a cancellation email at least 6 weeks before the expiration date) if you're going to be making a lot of train trips. Transportation was usually the biggest single expense for me. Overnight trains are often reasonably cheap, and if you bring a warm sweater and a jacket you can sleep on them. Then you arrive in your destination early in the morning and the world feels very shiny and new and ready for exploring.
Housing. Hostelworld, other hostel websites, AirBnB, whichever. When looking at hostels, consider proximity to the things you want to see and to transportation (e.g. in Salzburg I roomed at a hostel that was only two blocks from Hauptbahnhof because I had a 0600 bus).
Food. Bring your own food with you if you have a long trip or are just stingy (me). I got a box of granola bars the day before any trip and used those as breakfast and snacks. I think for my Rome trip I got two boxes. Go to grocery stores for food--it also will make you feel less like an obnoxious tourist. I felt particularly smug about getting most of my food from the Coop supermarket chain in Rome because I remembered the name from middle school Italian class. A big bag of crackers is easy to cart around without worrying about it melting or something. Bakeries are also good places to get cheap food. Get something to drink that refreshes you; my go-to was anything carbonated and citrus-flavored. Treat yourself to gelato if it's summer. Do try regional foods, if they fall within your dietary restrictions (e.g. I ate no wurst but I did eat a lot of potatoes).
If you're going to a city, any city, check if they have a tourism card/pass deal. These typically cover public transportation and some attractions/get you discounts on attractions. The Salzburg Card was the best deal I encountered (everything was free except a couple of special exhibits) while the Berlin Welcome Card deliberately leaves out Museum Island so just getting day passes for transportation made more sense. If you buy it from a person (e.g. at an airport or central station kiosk) they might give you a map also.
But if you can't count on that, download or print out a map so you know where you're going. I like being able to look at everything I want to do all at once and plan an efficient route (which may get thrown out midway through but hey, it happens). Before going, spend some time on Google Maps inputting places you want to go and how long it will take to get where. Of particular importance, plan out how you're going to get to your transportation back.
What to do? If you know someone who lives in or has been to the place you're visiting, ask them for advice. Look at the map and the city's tourism sites for inspiration. Go with what you like more than with what you're "supposed" to do. Are you going on vacation for yourself or for an audience? Examples: in Salzburg I visited the fortress twice, because I had written about it for Ubermadchen and it meant something to me. I skipped most of the Mozart- and Sound of Music-related stuff because I didn't have that connection. In Rome, I spent a whole lot of time in the Forum and Palatine area, even paying to get in a second time because I was not going to leave Rome without visiting the houses of Augustus and Livia. I didn't even try to go to the Vatican.
But if you're going someplace that doesn't have any particular personal meaning to you, that's fine too and you'll probably have a good time following travel guides. Still, if you have the choice, go someplace that means something to you.
Check the weather but no matter what bring a raincoat or umbrella. Go for maximum pockets but also be aware that pickpockets exist, so go for protectable pockets too. Because Germans tend to have very high standards of modesty, I ended up wearing long pants everywhere, even Rome, but this probably isn't necessary. Comfortable shoes. Hats are good--go for warmth if you're going someplace cold, go for sun protection if you're going someplace warm. Layers are good, especially if you're planning to be out doing things throughout the day. There are legit travel bloggers who can give pointers on the ideal wardrobe to bring to optimize simultaneously for a light pack and comfort.
Toiletries. I forgot to bring my toothbrush on multiple occasions. Bring a small towel, always (see: Hitchhikers' Guide to the Galaxy). My hair is very low-maintenance so for weekend trips I could get away with not bringing shampoo but you do you. If you get periods, bring the necessary materials even if you don't think it's likely that you'll need them. Highly recommend having a small bag that holds all of this stuff, so you can bring it all in one go to a hostel bathroom and not worry about leaving something behind.
Money. In some places, cash is strongly preferred to card (Germany). Other places card is okay. Different cards may have varying charges associated with international purchases so check that so you don't spend money unnecessarily. Make sure you know your PINs (seems obvious and yet there I was, staring dumbfounded at the ticket machine in Copenhagen central station at 8 in the morning). Bring only slightly more cash than you plan to spend in your wallet, in case you do get pickpocketed, and hide extra money in your phone case or anywhere else that seems safe.
Charge your phone, charge your camera if you have one. Bring along a portable charger if you'll be out for a long time/if your phone drains battery quickly, and charge that fully too. A bag for your chargers/cables is a good thing. Make sure you have lots of empty space for pictures. This was more of a concern for me than for most people since my old phone had very little storage on it. I was constantly deleting apps to make space for more photos and then redownloading them once I'd had a chance to move my photos to my computer.
Souvenirs. I like postcards. Postcards are small, light, cheap, easy to personalize. I wish I had picked up a few more generic postcards from various places so I'd have something to give to people who I realized after the fact might appreciate something of the kind. For people I didn't forget, it was usually pretty easy to look through an assortment of postcards and pick something they would like. Art museums generally have quality selections; tourist-geared vendors often have deals if you get multiple. I didn't get a lot of physical souvenirs, because suitcase space, but I tried to go for things that were small in size but personalized.
Re photos: there's a lot to be said about experiencing things in the moment and not necessarily documenting them. I took pretty much no photos of places such as the Holocaust Memorial in Berlin, or the concentration camps of Hamburg, for the same reason I don't talk to people when visiting such places--anything that could lead to greater performativity inhibits the sort of genuine response that I think these places require.
On the other hand, if you're visiting someplace to have fun, take photos all you want. Or if you see something interesting and want to document it. The act of composing a photo can also make you be more aware of what you're looking at, which is valuable. And even though I think you should let your wishes drive rather than the thought of what it looks like to others, there's nothing wrong with sharing photos of stuff you see. The biggest benefit, though, in my self-centered eyes at least, is being able to look through an archive of meaningful and happy memories.
Upcoming: a more philosophical post on the Grand Tour and the idea of travel being a necessary component of education.