So you are travelling to Budapest and want to do a photoshoot? I've lived and worked almost my whole life in Budapest, except a two year detour to Germany and as much travelling as I could manage. The capital city of Hungary features an exceptional amount of good locations that you can use even for free or for a very affordable price. This is my summary of the best places for shooting in Budapest:
Outdoor Locations
Budapest has many unique buildings and architectural styles that can be used as a backdrop if you are planning to shoot on the street. Let's start from the more explored and cliché places and move to the least likely ones:
The downtown area (District 5 and surroundings) features some romantic and classic buildings, but it might be a bit busy. If you are looking for a place to create street photos or some fashion-style outdoor pictures while doing touristy stuff, this is a good place to start. A local model could also have some locations in mind, so don't be shy to ask.
The huge river Danube and the bridges across it is a go-to place of starting photographers and of course tourists. It might be worth checking out with a model, but be prepared that this is the most common background on "street fashion" pictures taken in Budapest. That doesn't mean you shouldn't do it, everything can be exotic for someone who is not from around a certain place.
The castle district offers a bit more medieval scenery, while the 13th district was rebuilt after the second world war in a bauhaus style. There are numerous parks, although the most interesting is the Margit Island with ruins, flower gardens and the river on all sides.
If you are looking for something more modern, the metro line 4 is an odd, but surprisingly good choice. Every station is built in a modern style, designed by a famous hungarian architect, all of them are different and some of them are even pretty huge. You can start in one end, get off at every station, shoot a bit and keep going until you reach the other end... all with one ticket that costs about 400Ft (less than 1.50$).
Abandoned buildings, urbex locations and more rough looking scenery can be explored on the outskirts of the city, but with some prior investigation and some caution. I would not say Budapest is particularly unsafe, especially if you are in the prettier part of the city, but there are some sketchy neighbourhoods (like the infamous 8th district) and if you trespass into abandoned factories or buildings you might run into homeless people or unfriendly guard dogs. One popular destination is the Csepel Művek on the Csepel island on the south side of Budapest. This was a steelworks factory closed and abandoned since 1983.
Last, but not least: there are lots of forests around Budapest that are good for a nature themed photoshoot, especially in the north all the way up to Visegrád. Just pick a location on the map where it's green and explore! The relationship of nature and people (as you might be able to tell by my "In Wilderness" album) is one of my favourite topics to explore... if the weather is good enough too.
Indoor Locations
If you are planning to do some studio or indoor photography in Budapest, you are in luck, because the possibilities are endless. Local photographers usually don't bother having their own studio, so there's plenty of businesses who cater for creatives.
There is a wide range of rental studios, both furnished and with plain backdrops. They have a very reasonable price and you don't require complicated memberships or contracts (looking at you, Germany) - a basic unfurnished studio rent for an hour (with a few backdrops and all the lighting gear you need) would start around 2000-3000Ft (about 10$). The quality of the equipment is pretty good, although do ask if you need something specific... Every studio has at least 4-5 lights with all kinds of modifiers, but for example colour gels are not always a standard. If you have seen my pictures, you must know that I am a big fan of empty studios.
These studios are perfect if you want to do some portraits, glamour shots or you can always go with a furnished studio to do some boudoir or lifestyle pictures. Although I do have to admit I am not a huge fan of the furnished ones, they usually lack the clutter and spontaneity that gives the room a homely and realistic feel. But if you want a more styled environment, maybe go with a completely white baroque bedroom or a super modern living room, you will definitely find one on google.
Another solution could be hotels or airbnbs. Airbnbs are interesting, because many of the apartment owners are trying to attract tourists with interesting styles or just a homely vibe. And if you are not actually planning to use the place as accommodation, you have a much easier time finding something good. Number of beds or the location is not important, just the few features that can be used for your photoshoot. Once I have rented an apartment just because of the colour of the walls. Worth it.
For indoor location it is a good idea to book them in advance, but chances are you are going to find some free spots even spontaneously.
The list is endless, but these are my top choices for someone visiting. Now you only need a model... Luckily for you there are ways to find models even for free, the TFP scene is pretty good in Budapest - and nothing goes with the local architecture more than a local, home-grown model. Good luck!