Considering the very limited choice of bricks, I don't think you have much options.
The first is the obvious stacking of 1x2 bricks, which the added bonus that it can bend (slighly).
The second is the obvious stacking of 2x4 bricks, which is equally boring.
What I would suggest is to build windows in it, which you can easily achieve by mixing the two ...
Classic-Castle.com has a guide for making castle walls more visually appealing. Key points:
Different colours, shades and textures of bricks add subtle imperfections.
Break up the monotony with windows, doors, arrow slits, balconies and other structural features.
Use timber (brown/tan) as well as stone (grey) bricks and try out adding different materials.
Scale is the obvious answer. The Legoland model is huge, which means you're not seeing the brick-level quantisation as easily (quantisation is most obviously seen in mosaics but that works in 3D too).
Getting the same effect at smaller scales usually means a lot of SNOT and using sloped bricks. These days there is a huge range of slopes available, from 4 ...
Knight's Kingdom II - the guardian (picture taken from bricklink)
I searched on Bricklink catalog under, 'minifig leg assembly' using the keyword, 'brown,' using thumbnails. Only had two pages to look through.
If you have access to some Duplo elements, these make good "bulking" blocks for larger terrain sections - as the 2x2 and larger bricks fit over the top of the duplo studs you can build a fairly stable base using those, and then work on the sides and top with System elements as needed.
Otherwise it comes down to sensible building techniques such as starting ...
I don't build castles in general. But I do build Churches. For me I go very simple when it comes to breaking up the walls. I use an extreme amount of windows. Other shades of bricks. Often will use another color to add details or designs.
Good places to find parts include:
Thrift stores, car boot sales, jumble sales. Sometimes you get lucky.
eBay is a good general source for parts... as long as you can find what you're looking for.
LEGO's Pick-a-Brick (PAB) service is good for for common parts.
LEGO's replacement parts service is better for less common parts from newer sets. The range of ...
Yeah you pretty much have the two choices you outlined... hinges or make it so big that the squareness of the bricks melts into nothingness at that resolution.
OR... build your structure over tiles and use single studs, like at the ends of the ends of the hypotenuse of a 3-4-5 triangle... but that will be seriously flimsy the higher you build the walls, ...