Where to stay in York, UK (general guidelines, NOT specific hotels!)?

Here is how I'd start researching this, i'd have a list of requirements, higher up that last are things that are more important and easiest to research. For me i'd place on a bus route at the top of the list, the plan of staying in a nearby village and getting the bus won't work without a bus. If you Google "York bus map" you'll quickly find this pdf showing all the bus routes in York. As you can see the map is fairly zoomed in, showing the city centre and suburbs. However, many of the routes going of the edge say "to x". An additional thing to note on the key is that the routes with colour have a higher frequency, so I would go around the map and list out the "x" place with a coloured route map.

Another think that will slowly start to happen is you'll find some sites that you like. In addition to getting the bus in you could also consider getting the train into York, but where are some nearby stations? openrailway shows some nearby options.

Now probably the next item on your list, somewhere to park the car. In the outer-ling villages you are much more likely to find somewhere which offers carparking then if you get a room in a hotel in the centre of York. Your best bet is realy just google, but over time you'll likely find some sites that you like and may choose to visit directly, for example AirBnB is very popular for full property rentals, otherwise Googling B&B in x is still a great tool, especially for finding smaller and more local options.

You'll probably have other requirements to consider as well so I would keep going down the list, if once I've finished by list I and still have a number of possible options left I have a second things of items which are nice to have and I look for, but would go without if needed and are not deal breakers until there is only one left. I I can't find any accommodation that meets all of my essential criteria then I either have to decide to look into other locations and consider going to the original place in a few years or whether there is some of my essential criteria I can manage without for a short term if thats going to make the difference between a trip and no trip.

Another thing is practice, I plan and research far more trips then I can ever reasonably hope to go on, why not try your hand at Googling for some of the questions asked here and seeing if you can find the answer. It will help you answer your own questions more quickly and easily when you have them. Sometimes you might need to use some of Googles more complicated syntax (list). The "-" notation can be useful if i'm reaching a place with the same name as a larger place in another country. The AND/OR commands and quotes can also be useful to mix queries, for example "B&B in y "carpark"".

Some nearby villages with accommodation are on a railway route to York, such as Church Fenton.

Otherwise if you have a car you can drive from a village to a Park & Ride site, and then take a bus into York. The Park & Ride buses run frequently and their operating hours and locations are easy to google.

They are well signposted from the roads into York.

Consider staying in one of the towns near a railway station (e.g., along the Harrogate line).

The York railway station is adjacent to the National Railway Museum, and is itself a listed building. It's an easy walk to the centre and you will pass many sights along the way, including the York Minster, the city walls.

I'm suggesting this as an outside possibility for potential consideration, because of proximity to rail & trunk roads.

Rather than stay in a small village near York itself from where you'd have to commute the ever-popular York Ring Road to get to a Park & Ride, or even try driving into the parking-limited centre, you could actually stay on the outskirts of Leeds [or even the centre, but central Leeds is not car-friendly].

For instance, Cross Gates train station is 30 mins from the centre of York. Leeds central to York is about the same, because many of the trains don't stop at all the little stations on the way.

Cross Gates station is a 5 minute walk from the nearest Premier Inn - that of course is going to depend on whether you consider a 'business hotel' suitable, but it's one I've stayed at a lot because it's near where I grew up, so I use it when I visit, even though I've lived in London 25 years. The 'annexed pub' is my old local. Hotel parking is free, as is most of the surrounding area.
The area is quite suburban, reasonably quiet even allowing for the relatively busy Selby Road/Ring Road quite close by.
York is maybe 30 mins or so by car from there, as the A64 is minutes away from that hotel.